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Detecting unconscious bias in models, with R

Thu, 06/14/2018 - 21:18

(This article was first published on Revolutions, and kindly contributed to R-bloggers)

There's growing awareness that the data we collect, and in particular the variables we include as factors in our predictive models, can lead to unwanted bias in outcomes: from loan applications, to law enforcement, and in many other areas. In some instances, such bias is even directly regulated by laws like the Fair Housing Act in the US. But even if we explicitly remove "obvious" variables like sex, age or ethnicity from predictive models, unconscious bias might still be a factor in our predictions as a result of highly-correlated proxy variables that are included in our model.

As a result, we need to be aware of the biases in our model and take steps to address them. For an excellent general overview of the topic, I highly recommend watching the recent presentation by Rachel Thomas, "Analyzing and Preventing Bias in ML". And for a practical demonstration of one way you can go about detecting proxy bias in R, take a look at the vignette created by my colleague Paige Bailey for the ROpenSci conference, "Ethical Machine Learning: Spotting and Preventing Proxy Bias". 

The vignette details general principles you can follow to identify proxy bias in an analysis, in the context of a case study analyzed using R. The case study considers data and a predictive model that might be used by a bank manager to determine the creditworthiness of a loan applicant. Even though race was not explicitly included in the adaptive boosting model (from the C5.0 package), the predictions are still biased by race:


That's because zipcode, a variable highly associated with race, was included in the model. Read the complete vignette linked below to see how Paige modified the model to ameliorate that bias, while still maintaining its predictive power. All of the associated R code is available in the iPython Notebook.

GitHub (ropenscilabs): Ethical Machine Learning: Spotting and Preventing Proxy Bias (Paige Bailey)

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Mixed Models with Adaptive Gaussian Quadrature

Thu, 06/14/2018 - 20:26

(This article was first published on iProgn: Interactive Prediction Tools based on Joint Models, and kindly contributed to R-bloggers)

Overview

In this post, I would like to introduce my new R package GLMMadaptive for fitting mixed-effects models for non-Gaussian grouped/clustered outcomes using marginal maximum likelihood.

Admittedly, there is a number of packages available for fitting similar models, e.g., lme4, glmmsr, glmmTMB, glmmEP, and glmmML among others; more information on other available packages can also be found in GLMM-FAQ. GLMMadaptive differs from these packages in approximating the integrals over the random effects in the definition of the marginal log-likelihood function using an adaptive Gaussian quadrature rule, while allowing for multiple correlated random effects.

An Example: Mixed Effects Logistic Regression

We illustrate the use of the package in the simple case of a mixed effects logistic regression. We start by simulating some data:

We continue by fitting the mixed effects logistic regression for the longitudinal outcome y assuming random intercepts for the random-effects part. The primary model-fitting function in the package is the mixed_model(), and has four required arguments, namely,

  • fixed: a formula for the fixed effects,  
  • random: a formula for the random effects,  
  • family: a family object specifying the type of response variable, and  
  • data: a data frame containing the variables in the previously mentioned formulas.

 Assuming that the package has been loaded using library(“GLMMadaptive”), the call to fit the random intercepts logistic regression is:

By default, 11 quadrature points are used, but this can be adjusted using the nAGQ control argument. We extend model fm1 by also including a random slopes term; however, we assume that the covariance between the random intercepts and random slopes is zero. This is achieved by using the `||` symbol in the specification of the random argument. We fit the new model and compare it with fm1 using the anova() function that performs a likelihood ratio test:



 We further extend the model by estimating the covariance between the random intercepts and random slopes, and we use 15 quadrature points for the numerical integration:


Capabilities and Further Reading

The package offers a wide range of methods for standard generic functions in R applicable to regression models objects and mixed models objects in particular (e.g., fixef(), ranef(), etc.); more information can be found in the Methods for MixMod Objects vignette. In addition, some highlights of its capabilities:

  • It allows for user-defined family objects implementing not standardly available outcome distributions; more information can be found in the Custom Models vignette.
  • It can calculate fixed effects coefficients with a marginal / population averaged interpretation using the function marginal_coefs().
  • Function effectPlotData() calculates predictions and confidence intervals for constructing effect plots.

The development version of the package is available on the GitHub repository.

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Minor updates for ggseas and Tcomp R packages by @ellis2013nz

Thu, 06/14/2018 - 14:00

(This article was first published on free range statistics - R, and kindly contributed to R-bloggers)

Updates

I’ve made small updates to two of my R packages on CRAN: ggseas (seasonal adjustment on the fly for ggplot2 graphics) and Tcomp (tourism forecasting competition data). Neither of the packages changes in a noticeable way for most users.

I’ve written more about ggseas and Tcomp elsewhere. Given they’re both being updated at once, here’s a brief demo of them in action together.

There are 1,311 series in the list tourism in Tcomp. Each element of tourism contains some limited metadata about the series (for example its length, and how long the forecast is to be for), the original training data, and the “answer” in the form of the actual observations over the forecast period. These objects are of class Mdata, introduced in Rob Hyndmans’ Mcomp package, which comes with a convenient plotting method.

library(tidyverse) library(scales) library(ggseas) library(Tcomp) # default plot method for forecasting competition datasets of class Mdata par(bty = "l", font.main = 1) plot(tourism[["M4"]], main = "Series M4 from the tourism forecasting competition")

ggseas makes it easy to take a seasonal time series object (ie an object of class ts with frequency > 1), convert it into a data frame, and produce exploratory graphics with it. For example, here’s code to take the training data from that same forecasting competition object and compare the original with a seasonally adjusted version (using X13-SEATS-ARIMA for the seasonal adjustment), and a 12 month rolling average:

# convert a time series to a data frame the_data <- ggseas::tsdf(tourism[["M4"]]$x) # draw a graphic ggplot(the_data, aes(x = x, y = y, colour = 1)) + geom_line(aes(colour = "Original")) + stat_seas(aes(colour = "Seasonally adjusted")) + stat_rollapplyr(aes(colour = "12 month rolling average"), width = 12) + scale_colour_manual(values = c("Original" = "grey50", "Seasonally adjusted" = "red", "12 month rolling average" = "blue")) + theme(legend.position = c(0.2, 0.8)) + scale_y_continuous("Unknown units\n", label = comma) + labs(x = "", colour = "") + ggtitle("Comparison of statistical summary methods in plotting a time series", "Monthly series 4 from the Tourism forecasting competition")

Then the ggsdc function makes it easy to look at a decomposition of a time series. This really comes into its own when we want to look at two or more time series, mapped to colour (there’s an example in the helpfile), but we can use it with a univariate time series too:

ggsdc(the_data, aes(x = x, y = y), method = "seas") + geom_line() + ggtitle("Seasonal decomposition with `X13-SEATS-ARIMA`, `seasonal` and `ggseas`", "Monthly series 4 from the Tourism forecasting competition") + scale_y_continuous("Unknown units\n", label = comma) + labs(x = "")

I wrote the first version of the functions that later became ggseas in 2012 when working for New Zealand’s Ministry of Business, Innovation and Employment. We had new access to large amounts of monthly electronic transactions data and needed an efficient way to explore it on our way to developing what eventually became the Monthly Regional Tourism Estimates.

Reflections on CRAN

This experience and recent twittering on Twitter have led me to reflect on the CRAN package update process. Both these updates went through really smoothly; I’m always impressed at the professionalism of the volunteers behind CRAN.

I think CRAN is hugely important and an amazing asset for the R community. It’s really important that packages be published on CRAN. I think the mapping of dependencies, and the process for checking that they all keep working together, is the key aspect here.

ggplot2 apparently has more than 2,000 reverse dependencies (ie packages that import some functionality from ggplot2), all of them maintained more or less voluntarily. When major changes are made I can’t think of any way other than CRAN (or something like it) for helping the system react and keep everything working. For instance, I found out that the new ggplot2 v2.3.0 would break ggseas when I got an automated email advising me of this, from the tests Hadley Wickham and others working on ggplot2 ran to identify problems for their reverse dependencies. The RStudio community site was useful for pointing me (and others with similar issues) in the direction of a fix, and of course one uses GitHub or similar to manage issues and code version control, but in the end we need the centralised discipline of something like CRAN as the publication point and the definitive map of the dependencies. So, a big shout out to the volunteers who maintain CRAN and do an awesome job.

Reflections on testing

When a user pointed out a bug in the Tcomp package by raising an issue on GitHub, I was pleased with myself for using genuine test-driven development. That is, I first wrote a test that failed because of the bug:

test_that("series lengths are correct", { expect_equal(sum(sapply(tourism, function(s){length(s$x) - s$n})), 0) })

…and then worked on finding the problem and fixing it upstream. It’s such an effective way to work, and it means that you have a growing body of tests. Packages like Tcomp and ggseas go for years without me doing anything to them, so when I do have to go back and make a change it’s very reassuring to have a bunch of tests (plus running all the examples, and performing the checks for CRAN) to be sure that everything still works the way it’s meant to.

There’s not enough tests in the build process of those packages at the moment; the more experienced I get, the more I think “build more tests, and build them earlier” is one of the keys to success. This is just in code-driven projects either; I think there’s broad applicability in any professional situation, although the development and automation of tests is harder when you’re not just dealing with code.

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reticulate – another step towards a multilingual and collaborative way of working

Thu, 06/14/2018 - 11:00

(This article was first published on eoda english R news, and kindly contributed to R-bloggers)

R, Julia, Python – todays data scientists have the choice between numerous different programming languages, each with their own strengths and weaknesses. Would it not be convenient to bring those languages together and use the individual strength of each language? The package “reticulate” for R takes a step in this direction.


The reticulate package creates a Python connection for R which enables the user to combine both languages for an optimal result. This tutorial referring to the Python engine for R Markdown implemented by reticulate, we will illustrate the basic idea, functionality and usefulness of the engine.

As an in-depth tutorial with examples and a fictional use case, we include an HTML notebook which is created in R Markdown. You can find it here.

The weapon of choice – data analysis in your day-to-day work

It could all be so simple: Everyone speaks the same language, borders blur and collaborations become easier than ever. What seems to sound a bit dramatic, happens more often in the everyday life of a data scientist. Even though R can show its strengths from a statistical point of view, Python, as a multi-purpose language, is becoming increasingly popular in the data science scene. Because of its multifunctionality, it is used more and more frequently the programming language of choice. Therefore, it seems necessary to build a bridge between both languages and create a common space within a project.

The virtual bridge – the reticulate package

The reticulate package provides a Python connection for R. Users can execute Python code directly from the R console, load Python scripts into the R environment and make them usable for R. In addition, reticulate provides a Python engine for R Markdown, which is described in the following example in more detail.

Introduction – setup & Python chunks in R Markdown

The setup of reticulate is very simple. After installing the package as well as the preferred distribution (2.7x or 3.x) you can

library(reticulate) knitr::knit_engines$set(python = reticulate::eng_python)

install the Python engine. The chunks of code work as usual and every R chunk can be used for a Python chunk.

For example:

```{r testChunk_R, warning = FALSE, message = FALSE} Code ```

R chunk and

```{python TestChunk_Py, warning = FALSE, message = FALSE} Code ```

a Python chunk. But attention: The code executed as a Python chunk will not be loaded into the global environment! Access to functions and/ or variables from outside is only possible when knit is executed which means that the execution of chunk alone is not enough. In our corresponding HTML notebook you will find further examples for the implementation of functions in different languages.

Continuation – automatic type conversion and interconnectivity

Taken together, reticulate creates an appropriate bridge between two languages. This allows developers with different programming skills to work in the same document of a joint project, all that without having to translate code. Furthermore, the strengths of both languages can be used. To loosen up boundaries, reticulate also provides the possibility to access variables of other languages within the chunk of one language given.
The following code extract illustrates the function:

```{r chunk1_R} test_vector <- c(1, 2, 4, 4, 7, 3, 5) ``` ```{python chunk1_Py} num_four = r.test_vector.count(4) print „Der Vektor enthält “, num_four, „ mal die Zahl 4“ ``` ```{r chunk2_R} out_string = paste(„Richtig, der Vektor enthält“, py$num_four, „mal die Zahl 4“) print(out_string) ```

Reticulate automatically adapts types of respective language. For example, if chunk1_Py reads test_vector, the R type vector is converted into the equivalent Python type list.
Further type assignments can be found here.

Source_Python – the “hidden treasure” among functions

The ability to implement Python code directly into a document and use it across languages already provides us with a powerful tool for seamless collaboration. The hidden treasure among functions in the reticulate package can be found in the function source_python. This function reads a Python script and enables functions and variables for both languages within the markdown document. This operating mode is illustrated in the following example:

// Datei bubblesort.py def bsort(numbers): if(isinstance(numbers, list) == False or all(isinstance(p, (int, float)) for p in numbers) == False or len(numbers) == 0): print "Warning: Input must be of Type List, only numeric and have length >= 1" return for i in reversed(range(1, len(numbers))): for j in range(0, i): if(numbers[j] > numbers[j+1]): numbers = swap(numbers, j, j+1) return numbers def swap(numbers, id1, id2): temp = numbers[id1] numbers[id1] = numbers[id2] numbers[id2] = temp return numbers // Markdown Dokument ```{r setup_script} source_python(„bubblesort.py“) ``` ```{r sort_R} bsort(c(4, 3, 2, 1)) ``` Output: 1, 2, 3, 4 ```{python sort_Py} print bsort([4,3,2,1]) ```

Output: 1,2,3,4

The Python script bubblesort.py implements the bubblesort sorting algorithm under bsort(numbers) function. This implementation is then provided in the markdown document with source_python(„bubblesort.py“) and can be used by both languages, as shown above.

With this feature reticulate removes the last existing limitation. This allows developers to completely work in their preferred development environment and finally merge the results into a final document. Already existing Python scripts (e.g. scripts for database connection, deep learning algorithms, etc.) can be transferred seamlessly.

Use case – text mining with preparatory work

Considering the following fictional use case: an electronics retailer Elektro-X wants to sign an advertising contract with one of the three retailers Lenavu, Ace-Ar and AS-OS. In order to get a more detailed picture of the retailer’s satisfaction, Elektro-X starts a text mining project implemented in Python: shop reviews will be read and reviews for the retailer’s products will be searched. In addition, a function is provided for calculating an average rating of several reviews. Due to a lack of time, Elektro-X is unable to follow through with the project and hired eoda to finish this project. eoda has completed the analysis in R to gain access to ggplot for visualization while using the pre-work done in Python. eoda has transferred the project to R using the reticulate package. Furthermore, R has been used to visualize the evaluations and sentiment analysis.

Conclusion – the future of big data

Concluding, it can be said that packages like reticulate have the potential to significantly influence the big data industry and thus change its future. Especially service providers like eoda can benefit from barrier-free collaboration with their customers, as they can work on core problems more quickly without having to deal with possible problems beforehand. If you would like to work more efficiently on customer projects in the future, start considering language barriers solutions such as reticulate.

Would you like to know more about multilingual and collaborative working processes? We as data science specialists can help you take the next step. Contact us for more information at www.eoda.de

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R community update: announcing New Delhi useR meetup group

Thu, 06/14/2018 - 08:28

(This article was first published on R – Tech and Mortals, and kindly contributed to R-bloggers)

“The way to change the world is through individual responsibility and taking local action in your own community.” – Jeff Bridges Over the past few years, R’s adoption has grown rapidly throughout the world. Much of it can be attributed to the growth of ‘data science’ as a domain. But R’s popularity primarily exists because of its amazing community and their contributions. Be it through open source development, Twitter (#rstats), discussion forums or programs such as Google Summer of Code (GSoC), there are numerous channels for beginners and practitioners to interact with each other. I’ve had the opportunity to interact with members from R ecosystem through the previously mentioned channels. It has been wonderful to say the least. However, despite increasing popularity and user-base in India, the local community aspect has largely been missing. Even New Delhi, nation’s capital and a startup hub, lacks a strong community. There’d been efforts in the past to organize meetups and conferences but nothing really worked out. To address this, some R practitioners from the region have started a useR meetup group. We plan to host regular meetings, bring together existing R users and help introduce the language to beginners. You can find the meetup page link here. Also, we’re grateful to the R consortium for their support to the group through the R User Group and Small Conference Support Program. List of other groups which are part of the program can be found here. You can find more information about the program on their website. In addition to members, we’re also looking for speakers. Although we would prefer speakers to be present on venue, webinars can also work out. If you have useful ideas/learnings to share with the group or know someone else who could do the same, please reach out through mail or start a discussion on the meetup page. Again, do join the group if you want to be a part of this community. Here’s hoping to the community’s success. var vglnk = { key: '949efb41171ac6ec1bf7f206d57e90b8' }; (function(d, t) { var s = d.createElement(t); s.type = 'text/javascript'; s.async = true; s.src = '//cdn.viglink.com/api/vglnk.js'; var r = d.getElementsByTagName(t)[0]; r.parentNode.insertBefore(s, r); }(document, 'script'));

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A Comparative Review of the Deducer GUI for R

Thu, 06/14/2018 - 02:53

(This article was first published on R – r4stats.com, and kindly contributed to R-bloggers)

Introduction

Deducer is a free and open source Graphical User Interface for the R software, one that provides beginners a way to point-and-click their way through analyses. It also integrates into an environment designed to help programmers be more productive. Deducer is available on Windows, Mac, and Linux; there is no server version.

This post one of a series of reviews which aim to help non-programmers choose the Graphical User Interface (GUI) that is best for them. However, the reviews will include a cursory description of the programming support that each GUI offers.

Figure 1. JGR console with Deducer menus (left) and Deducer data viewer (right).

 

Terminology

There are various definitions of user interface types, so here’s how I’ll be using these terms:

GUI = Graphical User Interface specifically using menus and dialog boxes to avoid having to type programming code. I do not include any assistance for programming in this definition. So GUI users are people who prefer using a GUI to perform their analyses. They don’t have the time or inclination to become good programmers.

IDE = Integrated Development Environment which helps programmers write code. I do not include point-and-click style menus and dialog boxes when using this term. IDE users are people who prefer to write R code to perform their analyses.

 

Installation

The various user interfaces available for R differ quite a lot in how they’re installed. Some, such as jamovi, BlueSky, or RKWard, install in a single step. Others, such as the R Commander and Rattle, install in multiple steps. Advanced computer users often don’t appreciate how lost beginners can become while attempting even a simple installation. The HelpDesks at most are flooded with such calls at the beginning of each semester!

Deducer’s installation is quite complex:

  1. If you haven’t already done so, install the Java JRE. If you’re on Windows, I recommend the Windows x64 64-bit version.
  2. Download and install R. You should only need to keep the 64-bit version there too.
  3. Start R as an administrator, and from within it install Deducer and its companion IDE, the Java GUI for R (JGR, pronounced “jaguar”) using:
    packages(c(“JGR”,”Deducer”,”DeducerExtras”))
  4. Start JGR by submitting the commands:
    library(“JGR”)
    JGR()
  5. Within the JGR Console, start Deducer by choosing “Packages & Data> Package Manager” and clicking the checkboxes labeled “loaded” and “default” in front of both “Deducer” and “Deducer Extras”, then close the box.
  6. If you wish to get publication-quality output, download and install DeducerRichOutput from here.
  7. Finally, if you wish to start Deducer by clicking an icon (instead of typing two R commands) download the JGR launcher from here. If you have problems with this working start over while paying particular attention to where the instructions say, “as administrator.”

If your goal is to point-and-click your way through analyses, you probably won’t care for that much complexity. However, if your goal is to learn how to program in R, following those steps will help you on your way. Some of those steps are tasks you must learn when programming R.

 

Plug-in Modules

When choosing a GUI, one of the most fundamental questions is: what can it do for you? What the initial software installation of each GUI gets you is covered in the Graphics, Analysis, and Modeling sections of this series of articles. Regardless of what comes built-in, it’s good to know how active the development community is. They contribute “plug-ins” which add new menus and dialog boxes to the GUI. This level of activity ranges from very low (e.g. RKWard) through moderate (e.g. jamovi) to very active (e.g. R Commander).

Deducer has been in existence since 2009, and during that time nine plug-ins have been developed. Unfortunately there is no single place to go to find them. On the GUI’s “Packages & Data> GUI Add-ons” menu you’ll find four of them. Others are available here. The complete list of plug-ins that I could find is here:

  1. DeducerExtras: An add-on package containing a variety of additional analysis dialogs. These include: Distribution quantiles, single/multiple sample proportion tests, paired t-test, Wilcoxon signed rank test, Levene’s test, Bartlett’s test, k-means clustering, Hierarchical clustering, factor analysis, and multi-dimensional scaling
  2. DeducerPlugInScaling: Reliability and factor analysis
  3. DeducerMMR: Moderated multiple regression and simple slopes analysis
  4. DeducerRichOutput: writes results into true word processing tables with fonts and formatting
  5. DeducerSpatial: A GUI for Spatial Data Analysis and Visualization
  6. RDSAnalyst: Respondent Driven Sampling
  7. gMCP: (Experimental) A graphical approach to sequentially rejective multiple test procedures
  8. RGG: (Experimental) A GUI Generator
  9. DeducerText: (Experimental) Text Mining
  10. DeducerHansel: (Experimental) An add-on package which covers many methods common in econometrics, including binary logit, binary probit, and tobit estimates, and various time-series, panel, and spatial data methods. The time-series methods include cointegration analysis.
Startup

Some user interfaces for R, such as jamovi, start by double-clicking on a single icon, which is great for people who prefer to not write code. Others, such as R commander and Rattle, have you start R, then load a package from your library, then call a function. That’s better for people looking to learn R, as those are among the first tasks they’ll have to learn anyway.

On Deducer’s main web site, it recommends the following steps:

  1. Start R.
  2. Load the JGR package from your library by executing the command: “library(“JGR”)”.
  3. Start JGR by executing the command: “JGR()” and, if you followed the installation instructions above, JGR will start Deducer automatically. Both of the screens shown in Figure 1 will appear.

However, if you make it successfully through all seven installation steps described above, you can also start Deducer by double-clicking on the JGR Launcher icon.

 

Data Editor / Viewer

A data editor is a fundamental feature in data analysis software. It puts you in touch with your data and lets you get a feel for it, if only in a rough way. A data editor is such a simple concept that you might think there would be hardly any differences in how they work in different GUIs. While there are technical differences, to a beginner what matters the most are the differences in simplicity. Some GUIs, including jamovi, let you create only what R calls a data frame. They use more common terminology and call it a data set: you create one, you save one, later you open one, then you use one. Others, such as RKWard trade this simplicity for the full R language perspective: a data set is stored in a workspace. So the process goes: you create a data set, you save a workspace, you open a workspace, and choose a data set from within it.

Deducer’s data editor is named Data Viewer. That can be confusing since many well-known software packages – including RStudio, the R Commander, and SAS Studio – use the term “viewer” for tools that let you see but not edit the data. The first time I used Deducer, I spent an embarrassing amount of time trying to find the “data editor” when it was right under my nose!

Figure 2. Deducer’s Data Viewer with the “Data View” tab selected (upper left). I have right-clicked on the variable name of “q2” and it displayed a menu of tasks to perform.

You can start Deducer’s Data Viewer by choosing “File> New Data”. You then provide a name, and click OK. You’ll see it execute a command like, “mydata <- data.frame()” but the Data Viewer may not show you an empty spreadsheet. It tends to lock onto your last data set, but you can choose the drop-down menu labeled “Data Set” to get to the name of the one you just started to create. An empty version of the screen shown in Figure 2 will appear.

You can start entering data immediately, though the variables will be named V1, V2,… at first. Numeric and character data will be fine, but don’t enter any other type of variables yet, such as dates. Before you go very far, it’s important to click on the “Variable View” tab and fill in your metadata, such as variable names, Type and Factor Level (see Figure 3). When the metadata are filled in, the data editor may wipe out any existing data! For example, if you enter some dates like “8/31/2018” it will be stored as character. If you then switch to the Variable View, and click on Type for that variable, and choose “Date” from the drop-down menu, the editor will delete the exiting dates.

This combination of Data View/Variable View is a common one which was made popular by SPSS. In that software it offers great power by letting you copy metadata from one variable to dozens of others. So you might have survey data where, 1=”Strongly Disagree”, 2=”Disagree”,…”5=”Strongly Agree”. SPSS would allow you to define this for one variable, the copy it and paste it into many others. Deducer’s Variable View does not allow that. You must work one variable at a time, which gets quite tedious.

To open an existing data set, choose “File> Open Data”. If it doesn’t appear in the Data Viewer window, choose it from the Data Set drop-down menu.

Figure 3. Deducer’s Data Viewer with the “Variable View” tab selected (upper left). This displays and lets us edit the metadata for the same data as shown in Figure 2.

Saving the data is done with the standard “File> Save As” menu. You must save each one to its own file. While R allows multiple data sets (and other objects such as models) to be saved to a single file, Deducer does not. Its developers chose to simplify what their users have to learn by limiting each file to a single data set. However, you can also save or load multiple data sets by using JGR’s workspace save and open menu items. This strikes a good balance as beginners will relate to the simplicity of one-data-set-per-file, while advanced users will like the option to deal with more complex multi-object workspaces.

[Continued here…]

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Using R with Emacs and ESS

Thu, 06/14/2018 - 02:00

(This article was first published on The Devil is in the Data, and kindly contributed to R-bloggers)

A few years ago I ditched the spreadsheet in favour of writing code in R. During the process I learnt a valuable lesson: The steeper the learning curve, the larger the reward. My time invested in learning R has paid off in spades, and I now use the R language for all my numerical and qualitative analysis.

Most data scientists solve data problems with the R language using the RStudio IDE, a free and open-source Integrated Development Environment. Although RStudio is a great product, like all other software products, it’s functionality is limited to doing one thing well.

Since last year I use Emacs and once again the rule that a steep learning curve has a valuable reward has come true. Emacs is the Swiss army chainsaw of productivity, the ultimate killer app and also one of the oldest active pieces of software. Although it might seem that newer is better when it comes to software, Emacs has continuously evolved. The power of Emacs is its extensive functionality and virtually infinite customisability. Almost ninety per cent of all my computing activity now takes place within Emacs. I use it to write notes, manage my action lists, write e-mails, articles, books. The Org Mode package in Emacs is the working horse that undertakes many of these functions. Since recently also to write R code in Emacs.

To master Emacs to the level, I am at now has taken me a couple of months. Initially, the bewildering amount of keyboard shortcuts is a challenge, but your muscle memory will soon kick in, and your fingers will glide across the keyboard like an eagle.

Using R with Emacs and ESS: Org Mode with embeded R code to write an academic paper in APA format.

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Using R with Emacs and ESS: Org Mode with embedded R code to write an academic paper in APA format.

Using R with Emacs and ESS

The advantage of using Emacs over RStudio is that I can seamlessly switch between my notes, to-do lists, calendars and so on, while also developing code. There is no need to install, maintain and master multiple applications as Emacs cover almost all my computing needs. Just like R, Emacs includes thousands of packages that extend its functionality far beyond what one would expect from a text editor.

The disadvantage of Emacs compared to RStudio is that it is not as pretty and the screen more resembles an angry fruit salad than a slick material design. The image above shows my screen when I translated a paper about body image research into Org Mode with embedded R code. A temporary disadvantage is that there is a bit of preparation is required to enable coding in Emacs, but that is only a temporary hurdle and adds to the learning curve.

This article explains how to start Using R with Emacs and ESS (Emacs Speaks Statistics). The first section of this article provides links to resources on how to install Emacs on various platforms and how to enable it to start writing code in R with the ESS package. The second sections show how to use the R console and source files. The last section introduces literate programming by combining Org Mode and R and exporting the results to PDF, HTML etc.

Getting Started with Emacs

Installing Emacs depends on your operating system. A simple Google search will tell you what to do. The video playlist below shows how to install Emacs on Ubuntu, OS X or Windows 10. You will also need to install the R language on your machine, and if you like to create publication-quality output, the also include LaTeX.

Emacs needs an init file to define the packages that need to be loaded and to define several settings. A minimal-working init file can be downloaded from my GitHub repository.

To install packages, type M-x list-packages. This function displays all available packages. In Emacs-speak this means pressing the Alt (modify) key and the lowercase ‘x’ key, followed by ‘list-packages’ and return. You can find ESS by pressing ‘f’ and search for the package. Type ‘i’ to mark it for installation and press ‘x’ to execute the installation. The example init file loads the following packages that need to be manually installed:

  • ESS: Emacs Speaks Statistics.
  • ESS Smart Underscore: Smarter underscore for Emacs Speaks Statistics.
  • Org-Ref: org-mode modules for citations, cross-references, bibliographies in org-mode and useful BibTeX tools to go with it.
  • auto-complete: Auto Completion for GNU Emacs.
Using R with Emacs and ESS

To start using R with Emacs type M-x R RET. ESS will ask to nominate a working directory and opens a new buffer with the name *R*. You can now use the R console to write code as you are used to. You can open multiple instances of the R console with different working directories and environment, just like projects in RStudio.

Any file with the .R extension is now recognised as being written in the R language. This is a so-called Emacs major mode, which is the key functionality of Emacs. A major mode defines how a file is managed, whether it is an R file, an Org Mode file and so on.

One bit of useful information is that the underscore key is mapped to the <- assignment operator. If you need an underscore, you need to type it twice in a row. This can be annoying when you are an avid user of ggplot. The ess-smart-underscore package solves this issue by extending the functionality of ESS. You can install this package the same way you installed ESS itself. To enable it, add (require 'ess-smart-underscore) to your init file.

To write in a source file, you can create a .R file by typing C-x C-f (find-file function). Type the filename to create a new file, or when it already exists, open the file. You can now start writing R code as you would in any other editor. As soon as you evaluate code for the first time in a session, ESS will ask you what the starting project directory is, which is defaulted to the folder that your .R file is in. To evaluate the whole buffer, use C-c B, to evaluate a section use C-c c and to evaluate a line press M-RET.

To show the source file and the R console next to each other, type C-x 3 to split your window to show two buffers. You can then use C-x b to select the other buffer.

A disadvantage of using R in ESS is that there is no simple way to integrate plot outputs into the Emacs window. When I am iteratively working on a visualisation, I save it to a file and open it in a separate buffer, as shown in the screendump.

Using R with Emacs and ESS to Write an Academic Paper

Org Mode is the most popular extension of Emacs and is precompiled with current versions of the software. Org Mode is an extremely versatile text editing extension. I use it to manage my projects using a calendar and To-Do lists, I write notes, write books an articles. I have translated an article I previously wrote LaTeX and Sweave to Org Mode.

Org Mode works very well with LaTeX. You will need to write some code into your init file to set a template, after which writing LaTeX code is a breeze. The Org Babel package functions as an interface between Org Mode and R. Perhaps explaining this file in detail is a topic for a future post. You can view the most recent version of the Org File and the associated setting in the init file on my GitHub page.

Body Image research paper, written with Org Mode, R and LaTeX.

The post Using R with Emacs and ESS appeared first on The Devil is in the Data.

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Exploring European attitudes and behaviours using the European Social Survey

Thu, 06/14/2018 - 02:00

(This article was first published on rOpenSci - open tools for open science, and kindly contributed to R-bloggers)

Introduction

I never thought that I’d be programming software in my career. I started
using R a little over 2 years now and it’s been one of the most important
decisions in my career. Secluded in a small academic office with no one
to discuss/interact about my new hobby, I started searching the web for
tutorials and packages. After getting to know how amazing and nurturing
the R community is, it made me want to become a data scientist. So I set
out to do it. Throughout the journey I repeatedly found myself using
the European Social Survey (ESS from now on), a
really neat dataset that collects information on attitudes, beliefs and
behaviour patterns of diverse populations in more than thirty European
nations since 2002.

After seeing a niche in the R package community, I created the package
essurvey (previously ess in CRAN) to access this data easily from R.
The package was accepted in CRAN in September 2017 and was well received
among social scientists.

The 4th of March of 2018 I submitted the package to rOpensci, intimidated but
very excited about the peer review process. To my surprise, the process
was enriching, respectful and transparent, unlike my previous experience
in academic research.

First steps

Using the essurvey package is fairly easy. There are are two main
families of functions: import_* and show_*. They complement
each other and allow the user to almost never have to go to the ESS website.
The only scenario where you need to enter is to register your new account. If you haven’t registered,
create an account at http://www.europeansocialsurvey.org/user/new and
validate through your email inbox.

You can install the development version with

# install.packages("devtools") devtools::install_github("ropensci/essurvey")

or the stable version from CRAN with

install.packages("essurvey")

Let’s load the CRAN version and load it together with the tidyverse
set of packages to do some data manipulation.

library(essurvey) library(tidyverse)

Given that some essurvey functions require your email address, this
vignette will use a fake email but everything should work accordingly if
you registered with the ESS. We can set our email as an environment
variable with set_email

set_email("your@email.com")

Before we continue, let’s briefly explain some terminology
of the ESS data. Surveys are carried out every 2 years
and each survey is called rounds or waves. For example,
round one was the first round ever implemented, which dates
back to 2002. The second round followed up in 2004 and it’s
usually referred to as second round or second wave. There
are currently eight rounds freely available.

The ESS has over a thousand questions that include interesting
topics such as attitudes towards national governments, democracy,
immigration, nationalism, public policy as well demographic
and subjective health data on the participants of the survey.
Most of these questions use likert-type scales which means that
the possible answers to any given question range either from 0 through 5
or 0 through 10. For example, an average question would be something like:
how satisfied are you with democracy in your country? and the possible
answers range from 0 to 10 where 0 means very unsatisfied and 10 very satisfied.

Exploring government satisfacion in Spain

Let’s suppose you don’t know which countries or rounds (waves) are
available for the ESS. Then the show_* family of functions is your
friend.

To find out which countries have participated you can use
show_countries()

show_countries() ## [1] "Albania" "Austria" "Belgium" ## [4] "Bulgaria" "Croatia" "Cyprus" ## [7] "Czech Republic" "Denmark" "Estonia" ## [10] "Finland" "France" "Germany" ## [13] "Greece" "Hungary" "Iceland" ## [16] "Ireland" "Israel" "Italy" ## [19] "Kosovo" "Latvia" "Lithuania" ## [22] "Luxembourg" "Netherlands" "Norway" ## [25] "Poland" "Portugal" "Romania" ## [28] "Russian Federation" "Slovakia" "Slovenia" ## [31] "Spain" "Sweden" "Switzerland" ## [34] "Turkey" "Ukraine" "United Kingdom"

This function actually looks up the countries in the ESS website. If new
countries enter, this will automatically grab those countries as well.
Let’s check out Spain. How many rounds has Spain participated in? We can
use show_country_rounds()

sp_rnds <- show_country_rounds("Spain") sp_rnds ## [1] 1 2 3 4 5 6 7

Note that country names are case sensitive. Use the exact name printed
out by show_countries().

Using this information, we can download those specific rounds easily
with import_country.

spain <- import_country( country = "Spain", rounds = 1:7 )

Note: Since essurvey 1.0.0 all ess_* functions have been deprecated
in favour of the import_* and download_* functions.

spain will now be a list of length(rounds) containing a data frame
for each round. The import_* family is concerned with downloading the
data and thus always returns a list containing data frames unless only
one round is specified, in which it returns a tibble. Conversely, the
show_* family grabs information from the ESS website and always
returns vectors.

To download all rounds for a country automatically you can use
import_all_cntrounds.

import_all_cntrounds("Spain")

ESS datasets flag missing values differently between questions.
For example, questions with possible answers ranging from 0 through 5 have missing categories
such as “Don’t know” and “Refusal” coded as 7 and 8 and 9. But for questions with possible answers ranging from
0 through 10 missing values are coded as 77, 88 and 99. recode_missings accepts a
tibble as a main argument and automatically returns a new tibble
with all missing values recoded as NA. You should check out
?recode_missings for more details and elaborated examples.

Note: I urge the reader not to recode these categories to missing
without previously investigating the importance of these categories.

For example, let’s recode missing values in all Spanish waves, bind them
into one single tibble and visualize how satisfied are Spaniards with
their government. First, let’s extract a cleaner data.

semi_cleaned <- spain %>% map(recode_missings) %>% bind_rows() %>% mutate(name = str_sub(name, end = 4)) %>% select(name, stfgov) semi_cleaned ## # A tibble: 13,543 x 2 ## name stfgov ## ## 1 ESS1 0. ## 2 ESS1 0. ## 3 ESS1 5. ## 4 ESS1 5. ## 5 ESS1 4. ## 6 ESS1 7. ## 7 ESS1 2. ## 8 ESS1 2. ## 9 ESS1 3. ## 10 ESS1 3. ## # ... with 13,533 more rows

There we go. The scale of stfgov is between 0 and 10, where 0
means very unsatisfied with government and 10 very satisfied. Let’s
collapse that into smaller categories, calculate the percentage of
respondents within each category and visualize the change over time.

semi_cleaned %>% mutate(stfgov = case_when(stfgov <= 3 ~ "Low", between(stfgov, 4, 6) ~ "Mid", stfgov >= 7 ~ "High"), stfgov = factor(stfgov, levels = c("Low", "Mid", "High"))) %>% count(name, stfgov) %>% group_by(name) %>% mutate(perc = n / sum(n)) %>% ggplot(aes(name, perc, group = stfgov, colour = stfgov)) + geom_line() + theme_bw() + labs(x = "ESS rounds", y = "Satisfaction with Government (%)") + scale_colour_discrete(name = NULL)

Looks like Spaniards are increasingly unhappy with their government!

Exploring data by waves

Similarly to import_country, we can use other functions to download
rounds containing all countries. To see which rounds are currently
available, use show_rounds.

show_rounds() ## [1] 1 2 3 4 5 6 7 8

Similar to show_countries, show_rounds interactively looks up rounds
in the ESS website, so any future rounds will automatically be included.

To download selected rounds, you can use import_rounds.

selected_rounds <- import_rounds(1:7)

Alternatively, use import_all_rounds to download all available rounds.

all_rounds <- import_all_rounds()

To build on the previous example, we can compare two different countries
on their satisfaction with governments. Let’s map through each round,
select our columns of interest, filter for Spain and France, and bind
those data frames into one single tidy tibble.

semi_cleaned <- selected_rounds %>% map(~ select(.x, name, cntry, stfgov)) %>% map(~ filter(.x, cntry %in% c("ES","FR"))) %>% bind_rows() %>% mutate(name = str_sub(name, end = 4)) %>% recode_missings() semi_cleaned ## # A tibble: 26,524 x 3 ## name cntry stfgov ## ## 1 ESS1 ES 0. ## 2 ESS1 ES 0. ## 3 ESS1 ES 5. ## 4 ESS1 ES 5. ## 5 ESS1 ES 4. ## 6 ESS1 ES 7. ## 7 ESS1 ES 2. ## 8 ESS1 ES 2. ## 9 ESS1 ES 3. ## 10 ESS1 ES 3. ## # ... with 26,514 more rows

Now that we’ve got that down, let’s visualize the change over time by
calculating the percentage of respondents in each category for every
year/country combination and visualize the results.

semi_cleaned %>% mutate(stfgov = case_when(stfgov <= 3 ~ "Low", between(stfgov, 4, 6) ~ "Mid", stfgov >= 7 ~ "High"), stfgov = factor(stfgov, levels = c("Low", "Mid", "High"))) %>% count(name, cntry, stfgov) %>% group_by(name, cntry) %>% mutate(perc = n / sum(n)) %>% ggplot(aes(name, perc, group = stfgov, colour = stfgov)) + geom_line() + theme_bw() + labs(x = "ESS rounds", y = "Satisfaction with Government (%)") + scale_colour_discrete(name = NULL) + facet_wrap(~ cntry)

Spain and France follow very similar patterns although the changes are
much steeper in Spain! A more elaborate analysis would perhaps be
interested in finding out if this trend line is similar in other
countries.

Downloading data for Stata, SPSS and SAS users

To finish off, all import_* functions have an equivalent download_*
function that allows the user to save the datasets in a specified folder
in 'stata', 'spss' or 'sas' formats.

For example, to save round two from Turkey in a folder called
./my_folder, we use:

download_country("Turkey", 2, output_dir = "./myfolder/")

By default it saves the data as 'stata' files. Alternatively you can
use 'spss' or 'sas'.

download_country("Turkey", 2, output_dir = "./myfolder/", format = 'sas')

This will save the data to ./myfolder/ESS_Turkey and inside that
folder there will be the ESS2 folder that contains the data. The round
equivalent is download_rounds

Analyzing ESS data

Be aware that for analyzing data from the ESS survey you should take
into consideration the sampling and weights of each country/wave. The
survey package provides
very good support for this. A useful example comes from the work of
Anthony Damico and Daniel Oberski
here. This example
calculated percentages manually and appropriate statistical
inference
should consider the above.

Acknowledgments

The package was improved greatly thanks to the reviews of Thomas
Leeper
and Nujcharee
Haswell

and editorial skills of Maëlle Salmon. I am
indebted to their work. I would also like to thank Wiebke Weber at the
Research and Expertise Centre for Survey Methodology for giving support
and feedback in the development of the package.

The official package repository is at Github here.
If you find any bugs or would like to request a feature, please file an issue there. The package
is still very young and will most likely evolve in the near future. If you’re interested in contributing
to the development essurvey, don’t hesitate to file a pull request which I’ll gladly review.
One important feature that is still missing is being able to download the associated weight
data for each country/wave. These files are called “SDDF” and can be found in the ESS website.
For example, the SDDF files for some countries in round 6 can be found here.

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Announcing another slopegraph plotting function – June 14, 2018

Thu, 06/14/2018 - 02:00

(This article was first published on Chuck Powell, and kindly contributed to R-bloggers)

A couple of weeks ago I wrote a blog post about
slopegraphs
. There was some
polite interest and it was a good chance to practice my functional
programming skills
so
I decided to see if I could make a decent R function from what I had
learned. It’s in pretty good shape so I just pushed an update to
CRAN (it will take awhile to process). You can also get the latest version from GitHub.

The documentation for it is here. Longer
term I hope to move it here.

Overview

The package also includes other functions that I find useful for teaching
statistics as well as actually practicing the art. They typically are
not “new” methods but rather wrappers around either base R or other
packages and concepts I’m trying to master.

  • Plot2WayANOVA which as the name implies conducts a 2 way ANOVA and
    plots the results using ggplot2
  • PlotXTabs which as the name implies plots cross tabulated
    variables using ggplot2
  • neweta which is a helper function that appends the results of a
    Type II eta squared calculation onto a classic ANOVA table
  • Mode which finds the modal value in a vector of data
  • SeeDist which wraps around ggplot2 to provide visualizations of
    univariate data.
  • OurConf is a simulation function that helps you learn about
    confidence intervals
Installation # Install from CRAN install.packages("CGPfunctions") # Or the development version from GitHub # install.packages("devtools") devtools::install_github("ibecav/CGPfunctions") Credits

Many thanks to Dani Navarro and the book > (Learning Statistics with
R
)
whose etaSquared function was the genesis of neweta.

“He who gives up safety for speed deserves neither.”
(via)

A shoutout to some other packages I find essential.
  • stringr, for strings.
  • lubridate, for date/times.
  • forcats, for factors.
  • haven, for SPSS, SAS and Stata
    files.
  • readxl, for .xls and .xlsx
    files.
  • modelr, for modelling within a
    pipeline
  • broom, for turning models into
    tidy data
  • ggplot2, for data visualisation.
  • dplyr, for data manipulation.
  • tidyr, for data tidying.
  • readr, for data import.
  • purrr, for functional programming.
  • tibble, for tibbles, a modern
    re-imagining of data frames.
Leaving Feedback

If you like CGPfunctions, please consider leaving feedback
here
.

Contributing

Contributions in the form of feedback, comments, code, and bug reports
are most welcome. How to contribute:

  • Issues, bug reports, and wish lists: File a GitHub
    issue
    .
  • Contact the maintainer ibecav at gmail.com by email.
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Retracing Prenatal Testing Algorithms

Thu, 06/14/2018 - 00:00

(This article was first published on Theory meets practice..., and kindly contributed to R-bloggers)

Abstract

A good understanding of the statistical procedure used to calculate trisomy 21 (Down syndrome) risk in combined first trimester screening is a precondition for taking an informed decision on how to proceed with the screening results. For this purpose we implement the Fetal Medicine Foundation (FMF) Germany procedure described in Merz et al. (2016). To allow soon-to-become-parents an insight on what the procedure does and how sensitive conclusions are to perturbations, we wrote a small Shiny app as part of the R package trisomy21risk to visualize the results. We hope the tool can be helpful in the individual decision making process associated with first trimester screening.



This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. The markdown+Rknitr source code of this blog is available under a GNU General Public License (GPL v3) license from github.

Introduction

Biostatisticians predominantly analyse samples from populations of dead and diseased in the hope of substantiating answers to question aimed at preventing the adverse event in future individuals. Less common is the personalized \(n=1\) case, where -based on historical data- one has to choose an optimal test sequence or treatment regime for a specific individual. However, when interpreting your own laboratory values that is what you have to do – implicitly or explicitly!

In the case of first trimester prenatal testing for Down syndrome, aka. trisomy 21 (T21), parents are at the end of the screening routine given a piece of paper containing the results of a combined test. This consists of

  • the nuchal translucency (NT) measurement (in mm) of the fetus
  • concentration of the Pregnancy-associated plasma protein A (PAPP-A) and the human chorionic gonadotropin (β-HCG) hormone in the serum of the mother (measured in miU/ml)
  • (optional) results for other markers (e.g. ethnicity, maternal smoking, fetal heart rate, visibility of the nasal bone on the ultrasound)

From the biomarker values NT, PAPPA-A and β-HCG (and possibly additional markers) a risk for T21 is calculated and presented as an odds, say, 1:486. The question for the concerned soon-to-become-parents is now, whether to proceed with further tests – for example a DNA based approach in maternal blood plasma, a so called non-invasive prenatal test (NIPT) or, further down the line, an invasive amniotic fluid test. Recommendations for when to perform which additional screening steps exist and are discussed with the supervising gynecologist, but at the end its your choice as soon-to-become-parents.

The aim of this blog post is to illustrate how we failed to identify and understand the algorithm used to calculate the risk. As a consequence, we attempt a transparent and reproducible risk calculation algorithm based on the procedure described in Merz et al. (2016). To enhance risk communication we wrote an interactive Shiny app to calculate the risk, perform sensitivity analyses and graph distributions. Even though we are not experts on prenatal screening and have no access to any data, we hope such tools can inspire the experts or even be helpful in the individual decision making process associated with first trimester screening.

What is the FMF Algorithm 2012?

The first step in a scientific approach towards the problem is to understand, how the \(y\) in the reported \(1:y\) odds was determined. For this purpose the exemplary result report (in this case from a German prenatal diagnosis facility) contained a cryptic note to a "FMF Algorithm 2012". Unfortunately, no further reference to any scientific article, no link to a website with additional information nor any separate pamphlet was provided. Nevertheless, the soon-to-be-parents are assured that "The model for calculating the risk is based on intensive research work coordinated by the fetal medicine foundation (registered charity 1037116)". Cranking the google handle we found that there exists both an UK Fetal Medicine Foundation (FMF), which has the stated registered charity number, as well as a Fetal Medicine Foundation Germany. For reasons unclear to the outsider these two organizations use different risk algorithms: FMF-Germany uses a so called DoE-algorithm (DoE = Degree of extremeness) documented in the Merz et al. (2008), Merz et al. (2011) and Merz et al. (2016) (open-access) sequence of papers. In contrast FMF-UK uses software following "The First Trimester Screening module 2012 algorithm", which uses so called MoMs (multiples of the median). What this entails we could only find in a rogue access software manual: the document contains a large body of references sketching the different analysis components – in particular Kagan, Wright, Baker, et al. (2008) and Kagan, Wright, Valencia, et al. (2008) seem to cover the essentials components of the algorithm. However, for each component (nuchal translucency, β-HCG, PAPP-A, nasal bone, ductus venosus, heart rate, …) further references are given without it being clear, if or how they enter the algorithm. As an example, the FMF 2012 algorithm seems to analyze the NT measurement by a mixture model approach described in Wright et al. (2008) so the original approach in Kagan, Wright, Baker, et al. (2008) now seems obsolete. This might all be scientifically justified, but for an outsider it is impossible to retrace what is done: Even though we spent quite some time searching the FMF-UK website, which provides access to many of the FMF’s 957 scientific publications and watched videos about the algorithm, we could not find a more coherent document on what the FMF 2012 algorithm exactly is. Even the FMF on-line risk calculator does not contain a specific reference and seems to implement its own a variant of the algorithm (undocumented javascript source code).

At this point it is instrumental to recall paragraph V.3.3 in the German Gene Diagnostic Commission guideline for prenatal screening. It demands that the algorithm for the computation of such risks to be comprehensible, scientifically justified and published in a peer review process. In particular the guideline stresses that scientifically justified means:

Demanded is publication of the entire algorithm with detailed software specification, which precisely and comprehensible describes how the risks are calculated.

With such a strong statement by the guideline about the transparency and reproducibility of the algorithm the above hide-and-seek seems absurd.

Since we at the time of testing (wrongly?) believed that the FMF-Germany algorithm was the one used in the lab report and its papers appeared comprehensible enough for a re-implementation, we decided to scrutinize the FMF-Germany algorithm further in order to understand the computations. Aim was to understand how components influenced the calculation, perform a sensitivity analysis and better understand the uncertainty associated with the reported risk. The FMF Algorithm 2012 was expected to be similar in style.

The FMF-Germany Procedure – PRC 3.0

The procedure described in Merz et al. (2016) entitled Prenatal Risk Calculation (PRC) uses a classic Bayesian diagnostic approach, where one computes a posterior odds for the fetus having T21 as

\[
\text{Posterior odds} = \text{Likelihood ratio} \cdot \text{Prior odds}
\]

In the context of T21 first trimester screening, the prior odds is known to depend on maternal age and gestational age (at the time of screening) of the fetus. Tables for this can be found in, e.g., Table 4 of Snijders et al. (1999), which is shown below in the form of odds \(1:x\) for maternal age gaps of 5 years and selected gestational ages (measured in weeks). The gestational weeks relevant for the first trimester screening are the gestational weeks 10-13. Using a linear interpolation we obtain values for maternal and gestational age not covered in the table – see the trisomy21risk package code for details.

Table 1: Background risk in matrix form for T21 for maternal age (in years) and gestational age (in weeks) by Snijders et al. (1999).
Maternal Age W10 W12 W14 W16 W20 W40 20 983 1068 1140 1200 1295 1527 25 870 946 1009 1062 1147 1352 30 576 626 668 703 759 895 35 229 249 266 280 302 356 40 62 68 72 76 82 97 45 15 16 17 18 19 23

From the table we see that the background risk increases with maternal age and decreases with gestational age. The latter is related to the fact that a T21 fetus has an increased risk of spontaneous abortion. One criticism of using the maternal age as background risk is that age is merely a proxy for processes and complications not well understood. From a certain maternal age, it is thus almost impossible to get a test-negative result, even though most babies born by mothers that age are healthy (Schmidt et al. 2007).

The above formula for the posterior odds means that we can compute the posterior probability for T21 as \[
\text{Posterior probability} = \left( 1 + \frac{1}{\operatorname{LR}_{joint}} \cdot \frac{1-\text{Prior probability}}{\text{Prior probability}} \right)^{-1}.
\] The complicated part of the analysis is now to determine the joint likelihood ratio between the aneuploid pregnancies (i.e. T21 pregnancies) vs. euploid pregnancies (i.e. non-T21 pregnancies) as a function of the three biomarkers. In some cases additional continuous or binary markers indicating for example the smoking status, the visibility of the nasal bone on the ultrasound or the ductus venosus blood flow (expressed as pulsatility index) are used to distinguish further. For sake of exposition we use the presence of a nasal bone on the ultrasound as additional marker.

In Merz et al. (2011) and Merz et al. (2016) the likelihood ratio between aneuploid and euploid pregnancies is broken down into individual components by assuming that the random variables describing the observed value for the four risk factors are independent given ploidy (i.e. the T21 status):

\[
\begin{align*}
\operatorname{LR}_{joint} &= \frac{f_{\text{aneu}}(y_{\text{NT}}, y_{\beta\text{-HCG}}, y_{\text{PAPP-A}}, y_{\text{nasal bone}})}{f_{\text{eu}}(y_{\text{NT}}, y_{\beta\text{-HCG}}, y_{\text{PAPP-A}}, y_{\text{nasal bone}})} \\
&=
\left(
\frac{f_{\text{aneu}, \text{NT}}(y_{\text{NT}})}{f_{\text{eu}, \text{NT}}(y_{\text{NT}})}
\right)
\cdot
\left(
\frac{f_{\text{aneu}, \beta\text{-HCG}}(y_{\beta\text{-HCG}}}{f_{\text{eu}, \beta\text{-HCG}}(y_{\beta\text{-HCG}})}
\right)
\cdot
\left(
\frac{f_{\text{aneu}, \text{PAPP-A}}(y_{\text{PAPP-A}})}{f_{\text{eu}, \text{PAPP-A}}(y_{\text{PAPP-A}})}
\right)
\cdot
\left(
\frac{f_{\text{aneu}, \text{nasal bone}}(y_{\text{nasal bone}})}{f_{\text{eu}, \text{nasal bone}}(y_{\text{nasal bone}})}
\right)\\
&= \operatorname{LR}_{\text{NT}} \cdot \operatorname{LR}_{\beta\text{-HCG}} \cdot \operatorname{LR}_{\text{PAPP-A}} \cdot \operatorname{LR}_{\text{nasal bone}}
\end{align*}
\]

In the above, the \(f\)‘s denote the respective probability density functions, which may depend on covariates such as gestational age (at the time of measuring) or the weight of the mother. In Appendix 1 we look in detail at how the likelihood ratio is computed for the NT measurement. The procedure is then analogous for the β-HCG and PAPPA-A markers – one difference is, though, that Merz et al. (2016) extends the analysis to allow for these β-HCG and PAPPA serum markers to be collected at a gestational age 2-3 weeks earlier than the NT measurement, because the discrimination is better for these biochemistry markers at this gestational age. Altogether, if the prior odds is given in the form \(1:x\) then \(\operatorname{LR}_{joint}\) is the factor multiplied onto \(x\) to get the posterior odds in the form of \(1:y\). That means that if \(\operatorname{LR}_{joint}>1\) then the marker values are such that the risk for T21 increases.

R Implementation

The trisomy21 function in the trisomy21risk package performs all the computations to take one from the prior odds, covariates and biomarker values to the posterior odds.

formalArgs(trisomy21risk::trisomy21) ## [1] "age" "weight" "crlbe" "crl" "nt" "pappa" ## [7] "betahCG" "nasalbone" "background"

In the above age (in years) and weight (in kg) refer to the mother, crl is the crown-rump-length (measured in mm) at the time of the NT measurement and crlbe is the crown-rump-length at the time of the biomarker measurement. The pappa and betahCG concentrations are both measured in miU/ml. Finally, background is the \(x\) of the prior odds \(1:x\). The function outputs a named list of which one element is the posterior odds (in the form of \(1:y\)).

Philosophical note: The obtained posterior odds for the risk from the analysis is technically not really your individual risk, but the proportion in a population of, say, 1000 individuals with the same (measurable) covariate configuration as your own. As Bayesians we, however, feel a certain pain towards such a frequentist interpretation of the probability concept at the end of a Bayesian analysis. Believing that assumptions and model choice are subjective, we dare say that the obtained number has become your risk as soon as you have to deal with the number.

We can now compare our results to, e.g., the 12 randomly selected patients listed in Tab. 5 of Merz et al. (2016). Note that the first patient has a posterior odds of 1:486, which we used as example patient in the introduction. Results are compared in two ways:

  • using the background risk as specified in the Background column by the paper and comparing our result (Column: our_Post) to the \(y\) of the posterior odds stated in the paper (Column: Post).
  • Manually calculate the background risk using maternal age and gestational age by interpolation of the Snijders table (Column: our_Background) and compare our result (Column: our_Post_Back) with the result of the paper (Column: Post).
##Load numbers from Tab. 5 of the paper (contains 12 patients) tab5 <- read.csv2(file.path(filePath,"merzetal2015-tab5.csv")) ##Compute our own results for each patient tab5 %<>% rowwise %>% do({ ##Arguments for the call to the trisomy21 function args <- list(age=.$Age, weight=.$Weight, crlbe=gestage2crl(.$CRLBE), crl=gestage2crl(.$CRL), nt=.$NT, pappa=.$PAPP_A, betahCG=.$beta_hCG, nasalbone="Unknown", background=.$Background) ##Manually compute the prior odds our_Background <- background_risk(age_mother=.$Age, gestage=.$CRL/7) ##Call the trisomy function with the two type of background odds post <- do.call("trisomy21",args=args) post_back <- do.call("trisomy21",args=modifyList(args, list(background=our_Background))) ##Return result data.frame(., our_Post = post$onetox, our_Background=round(our_Background,digits=0), our_Post_Back=post_back$onetox) }) Table 2: Table 5 in Merz et al. (2016) annotated with our manually computed results. Note: The gestational ages (CRL and CRLBE) are now suddenly measured in gestation week and not mm.
Age Weight CRLBE CRL NT PAPP_A beta_hCG Background Post our_Post our_Background our_Post_Back 37 74.5 58 86 2.3 0.330 52.5 145 486 494 140 477 33 65.1 58 86 2.0 0.526 124.7 349 1022 1043 352 1052 27 48.6 59 88 1.2 0.210 71.6 876 2901 3412 752 2931 23 65.4 58 88 1.9 0.725 96.0 1021 13238 13583 915 12175 42 72.8 59 89 2.0 0.359 77.0 45 176 208 35 162 37 69.0 58 89 1.8 0.241 47.2 147 1355 1526 140 1453 36 84.4 58 90 2.0 0.290 51.9 225 2198 2332 180 1865 41 61.6 55 90 1.7 0.219 84.6 55 264 285 47 243 30 57.6 59 91 1.6 0.349 75.3 677 6329 6990 576 5947 26 64.7 59 92 1.6 0.230 73.9 945 3983 4506 811 3868 35 74.3 59 92 1.5 0.399 69.6 233 5072 5691 229 5593 34 51.6 58 93 2.1 0.563 142.4 338 902 966 287 821

Altogether, we observe that the results do not fully agree, but are in most cases of the same magnitude. Even when using the same prior odds there are still differences, which can be explained by the use of different polynomial \(\hat{y}(x)\) forms for NT, PAPP-A and β-HCG, because of problems reproducing the results with the polynomials stated in Merz et al. (2016) – see Appendix 2. Furthermore, the interpolation of the background risks from the Snijders table (Column: our_Background) deviates: Apparently, a different interpolation procedure is used by Merz et al. (2016) – we could not find an explicit mentioning of how this part is done.

Shiny App

For better illustration we have written a small Shiny app in order to get a better feeling of what the algorithm does, for example, by performing a sensitivity analysis where one changes one measurement value slightly. The App is available from:


https://hoehle.shinyapps.io/t21app/

and can also be ran locally, by installing the trisomy21risk package from github:

devtools::install_github("hoehleatsu/trisomy21risk") trisomy21risk::runExample() Screenshots

Computing the T21 risk:


As example: the NT measurement in the ultrasound image is subject to some measurement error – even the most skilled operator has difficulties obtaining errors smaller than 0.2 – 0.3 mm. With the app we can easily investigate how such measurement error influences the calculated risk. Another aspect to investigate is the influence of the background risk from maternal age.

Visualizing the likelihood ratios:


Discussion

With a cut-off of value of 1:150 for the posterior odds, Merz et al. (2016) report a detection rate for T21 of 86.8% and a false positive rate of 3.42%. The 1:150 is also the threshold they suggest for further invasive action. For posterior odds up to 1:500 the suggestion in Merz et al. (2011) is to perform additional sonographic investigations in the second trimester. Nowadays, one would typically perform a NIPT.

Was the algorithm for the computation of the risk detailed and comprehensive as demanded by the Gene Diagnostic Commission? Well, since we -despite quite some effort- were not able to find a full description of the FMF 2012 algorithm and, as described in Appendix 2, were not able to reproduce the numbers in Merz et al. (2016), we say: no. As algorithms become more complex and -as for the FMF 2012 algorithm- contain the combined insights of 10+ scientific papers, transparency starts with a single easy-to-find accessible document coarsely describing the overall algorithm. The FMF software manual, which apparently is not accessible to the public, would have been a start. Even better would be an open-source reference implementation! To this date it remained unclear how the standard NT, PAPP-A and β-HCG measurements entered the analysis and if additional components (ethnicity? smoking status? nasal bone? heart rate? ductus flow?) entered the risk calculation. Similarly, publishing a statistical description of the FMF-Germany algorithm in open-access articles, e.g. such as Merz et al. (2016), is a step in the right direction, however, some of the equations in the paper were either erroneous or intentionally kept so vague, the algorithm became impossible to reconstruct. Altogether, transparency and risk communication for this sensitive diagnostic procedure should be improved to meet guideline standards.

What do you do with the obtained posterior risk once you have it? This is indeed a very personal decision, which make the shortcomings of statistics clear: Statisticians can annotate even the most unlikely event with a probability of happening, but the probability is rarely zero, so it’s your personal threshold for likely enough balanced against the ethics and personal beliefs of what to do if, which determines your actions… In this \(n=1\) context the reported risk might merely be a hypothetical number – at most its rough magnitude is of interest. However, from a system perspective \(n\) is much larger, so everything possible should be done such that the probabilistic forecast is both calibrated and sharp and that the recipient(s) knows what this number entails.

Postscript

Further information about first trimester screening can be obtained from the Fetal Medicine Foundation. In particular their book about the 11-13 weeks scan (available in several languages) is very helpful (Nicolaides 2004). As mentioned the FMF-UK offers a web-based trisomies risk assessment calculator. Similarly, the FMF-Germany has their own website with information – apparently it is now also possible to obtain a demo version of their risk calculation software PRC 3.0.

Appendix

The mathematical details of the post and our troubles reproducing the results of Merz et al. (2016) are described in two separate Appendixes,

Literature

Kagan, K. O., D. Wright, A. Baker, D. Sahota, and K. H. Nicolaides. 2008. “Screening for trisomy 21 by maternal age, fetal nuchal translucency thickness, free beta-human chorionic gonadotropin and pregnancy-associated plasma protein-A.” Ultrasound Obstet Gynecol 31 (6): 618–24.

Kagan, K. O., D. Wright, C. Valencia, N. Maiz, and K. H. Nicolaides. 2008. “Screening for trisomies 21, 18 and 13 by maternal age, fetal nuchal translucency, fetal heart rate, free beta-hCG and pregnancy-associated plasma protein-A.” Hum. Reprod. 23 (9): 1968–75.

Merz, E., C. Thode, A. Alkier, B. J. Hackelöer, M. Hansmann, G. Huesgen, P. Kozlowski, M. Pruggmaier, and S. Wellek. 2008. “A New Approach to Calculating the Risk of Chromoso- Mal Abnormalities with First-Trimester Screening Data.” Ultraschall in Der Medizin / European Journal of Ultrasound 29: 639–45. doi:10.1055/s-2008-1027958.

Merz, E., C. Thode, B. Eiben, and S. Wellek. 2016. “Prenatal Risk Calculation (PRC) 3.0: An Extended DoE-Based First-Trimester Screening Algorithm Allowing for Early Blood Sampling.” Ultrasound International Open 2: E19–E26. doi:10.1055/s-0035-1569403.

Merz, E., C. Thode, B. Eiben, R. Faber, B. J. Hackelöer, G. Huesgen, M. Pruggmaier, and S. Wellek. 2011. “Individualized Correction for Maternal Weight in Calculating the Risk of Chromosomal Abnormalities with First-Trimester Screening Data.” Ultraschall in Der Medizin/European Journal of Ultrasound 32: 33–39. doi:http://dx.doi.org/10.1055/.

Nicolaides, K. H. 2004. The 11–13\(^{+6}\) Weeks Scan. Fetal Medicine Foundation, https://fetalmedicine.com/synced/fmf/FMF-English.pdf.

Schmidt, P., J. Rom, H. Maul, B. Vaske, P. Hillemanns, and A. Scharf. 2007. “Advanced first trimester screening (AFS): an improved test strategy for the individual risk assessment of fetal aneuploidies and malformations.” Arch. Gynecol. Obstet. 276 (2): 159–66.

Snijders, R. J., K. Sundberg, W. Holzgreve, G. Henry, and K. H. Nicolaides. 1999. “Maternal age- and gestation-specific risk for trisomy 21.” Ultrasound Obstet Gynecol 13 (3): 167–70.

Wright, D., K. O. Kagan, F. S. Molina, A. Gazzoni, and K. H. Nicolaides. 2008. “A mixture model of nuchal translucency thickness in screening for chromosomal defects.” Ultrasound Obstet Gynecol 31 (4): 376–83.

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Anomaly Detection for Business Metrics with R

Wed, 06/13/2018 - 23:43

(This article was first published on R language – AnalyzeCore by Sergey Bryl' – data is beautiful, data is a story, and kindly contributed to R-bloggers)

The larger and more complex the business the more metrics and dimensions. One day you understand that it is impossible to track them with only your eyes.The larger and more complex the business the more metrics and dimensions. One day you understand that it is impossible to track them with only your eyes. Reducing the number of metrics and/or dimensions can prevent us from tracking all aspects of the business or analyzing aggregated data (for example, without dimensions), which can substantially smooth out or hide the anomalies. In such a situation, the detection of any anomalies after the actual occurrence can either be missed or have a significant time gap. Therefore, we have to react immediately in order to learn about the event as soon as possible, identify its causes, and understand what to do about it. For this, we can use the Anomaly Detection system and identify abnormal values, collect the corresponding events centrally, and monitor a much larger number of metrics and dimensions than what human capabilities allow.

In this article, by  business metrics, we mean numerical indicators we regularly measure and use to track and assess the performance of a specific business process. There is a huge variety of business metrics in the industry: from conventional to unique ones. The latter are specifically developed for and used in one company or even just by one of its teams. I want to note that usually, a business metrics have dimensions, which imply the possibility of drilling down the structure of the metric. For instance, the number of sessions on the website can have dimensions: types of browsers, channels, countries, advertising campaigns, etc. where the sessions took place. The presence of a large number of dimensions per metric, on the one hand, provides a comprehensive detailed analysis, and, on the other, makes its conduct more complex.

Anomalies are abnormal values of business indicators. We cannot claim anomalies are something bad or good for business. Rather, we should see them as a signal that there have been some events that significantly influenced a business process and our goal is to determine the causes and potential consequences of such events and react immediately. Of course, from the business point of view, it is better to find such events than ignore them.

It is worth to say that such Anomaly Detection system will also signal the significant changes expected by the user, not the system. That is, the events you initiated in order to influence the business and the causes you are aware of. An example is running an irregular promo through an email campaign and expecting traffic to grow on a landing page from the same channel. Getting such a signal is also useful in terms of confirming that the promo works.

To date, a number of analytical tools have built-in systems for detecting anomalies. For example, Google Analytics has such a system.

However, in case you:

  1. collect raw data that does not transfer to an analytical tool with an integrated anomaly detection system,
  2. want to choose and combine algorithms in order to determine anomalies,
  3. want to tune the system parameters (for instance, setting a higher or lower threshold for values that will be defined as anomalies),

perhaps, you want to do something similar to the system I use.

Therefore, we will study four approaches for identifying anomalies in business metrics using the R language. I also will assume that we deal with unlabeled data, i.e. we did not know whether what historical values were anomalies.

For a practical example, I have extracted web data that looks like the following table:

In addition, I have added the aggregated values for each date and the metric “number of goals per session”. Then, we can visualize the metrics on the time axis separately with the following code:

click to expand R code

library(tidyverse) library(reshape2) library(lubridate) library(purrrlyr) library(ggrepel) # devtools::install_github("twitter/AnomalyDetection") library(AnomalyDetection) # install.packages("IsolationForest", repos="http://R-Forge.R-project.org") library(IsolationForest) # loading raw data df <- read_csv('data.csv') # summarizing metrics by dates df_tot <- df %>% group_by(date) %>% summarise(sessions = sum(sessions), goals = sum(goals)) %>% ungroup() %>% mutate(channel = 'total') # bindind all together df_all <- rbind(df, df_tot) %>% mutate(goals_per_session = ifelse(goals > 0, round(goals / sessions, 2), 0)) # visualizing metrics ggplot(df_all, aes(x = date)) + theme_minimal() + facet_wrap(~ channel) + geom_line(aes(y = sessions), color = 'blue') + geom_line(aes(y = goals), color = 'red') ggplot(df_all, aes(x = date, y = goals_per_session)) + theme_minimal() + facet_wrap(~ channel) + geom_line(color = 'darkgreen')

As you can see, we have data from August to November and at the end of September, in general, there was a significant spike in three of the five channels and in total as well. There are less significant spikes in Social and Direct.

Below are the different patterns in the “goals_per_session” metric:

Ok, let’s see what we can do with this example:

#1 – Model approach
The idea is the following: we create a model based on historical data and observations on which the model is the most mistaken are anomalies.

In practice, we measure a business metrics on a regular basis, usually daily. This means that they have a time series nature. Therefore, we can use a time series model and if the predicted value is significantly different from the actual value, then we detect the anomaly. This approach is good for metrics with obvious seasonal fluctuations. In our example, these are numbers of sessions and goals for the main channels. For the “goals_per_session” metric, this approach may not be as effective.

There are a lot of packages for time series modeling in R but, considering our goal of finding anomalies, I recommend using one of the ready-made solutions, for instance, AnomalyDetection package.

Let’s start with the simple example of analyzing Direct traffic:

click to expand R code

##### time series modeling ##### # simple example df_ts <- df_all %>% # the package works with POSIX date format mutate(date = as.POSIXct(date, origin = "1970-01-01", tz = "UTC")) df_ts_ses <- df_ts %>% dcast(., date ~ channel, value.var = 'sessions') df_ts_ses[is.na(df_ts_ses)] <- 0 # example with Direct channel AnomalyDetectionTs(df_ts_ses[, c(1, 3)], max_anoms = 0.05, direction = 'both', e_value = TRUE, plot = TRUE) # 5% of anomalies AnomalyDetectionTs(df_ts_ses[, c(1, 3)], max_anoms = 0.1, direction = 'both', e_value = TRUE, plot = TRUE) # 10% of anomalies

As you can see, we can change the number of anomalies by shifting a threshold of the percent of anomalies we are allowed to detect.

In order to scale this approach to all metrics, we can map the function to all of the dimensions of all of the metrics with the following code:

click to expand R code

# scaled example df_ts <- df_all %>% # removing some metrics select(-goals_per_session) %>% # the package works with POSIX date format mutate(date = as.POSIXct(date, origin = "1970-01-01", tz = "UTC")) %>% # melting data frame melt(., id.vars = c('date', 'channel'), variable.name = 'metric') %>% mutate(metric_dimension = paste(metric, channel, sep = '_')) %>% # casting dcast(., date ~ metric_dimension, value.var = 'value') df_ts[is.na(df_ts)] <- 0 # anomaly detection algorithm as a function df_ts_anom <- map2(df_ts %>% select(1), df_ts %>% select(c(2:ncol(.))), function(df1, df2) { AnomalyDetectionTs(data.frame(df1, df2), max_anoms = 0.1, direction = 'both', e_value = TRUE) } ) # extracting results df_ts_anom <- lapply(df_ts_anom, function(x){ data.frame(x[["anoms"]]) }) # adding metric names and binding all metrics into data frame names(df_ts_anom) <- colnames(df_ts[, -1]) df_ts_anom <- do.call('rbind', df_ts_anom)

 

#2 – Statistical approach
From the statistical point of view, anomalies are extreme values or outliers. There is a number of ways and corresponding functions in R to identify such values. And, of course, the use of certain criteria should be made based on the properties of the sample.

I apply the statistical approach to analyze such indicators as “goals_per_session” in our example. This indicator has a close to normal distribution over the more popular channels and, accordingly, one, for example, can use an interquartile distance to determine the outliers.

click to expand R code

ggplot(df_all, aes(x = goals_per_session)) + theme_minimal() + facet_wrap(~ channel) + geom_histogram(binwidth = 0.01)

Often in practice, I am less concerned with whether the value is an outlier than whether it is too high or low compared to other days. For such a case, you can simply use the lower and upper, for example, 5% percentile (0-5% and 95-100% ranges). Both approaches can be implemented and the results are visualized with the following code:

click to expand R code

df_stat_anom <- df_all %>% # select the metrics select(-sessions, -goals) %>% group_by(channel) %>% mutate(is_low_percentile = ifelse(goals_per_session <= quantile(goals_per_session, probs = 0.05), TRUE, FALSE), is_high_percentile = ifelse(goals_per_session >= quantile(goals_per_session, probs = 0.95), TRUE, FALSE), is_outlier = case_when( goals_per_session < quantile(goals_per_session, probs = 0.25) - 1.5 * IQR(goals_per_session) | goals_per_session > quantile(goals_per_session, probs = 0.75) + 1.5 * IQR(goals_per_session) ~ TRUE, TRUE ~ FALSE) ) %>% ungroup() ggplot(df_stat_anom, aes(x = date, y = goals_per_session)) + theme_minimal() + facet_wrap(~ channel) + geom_line(color = 'darkblue') + geom_point(data = df_stat_anom[df_stat_anom$is_outlier == TRUE, ], color = 'red', size = 5, alpha = 0.5) + geom_point(data = df_stat_anom[df_stat_anom$is_low_percentile == TRUE, ], color = 'blue', size = 2) + geom_point(data = df_stat_anom[df_stat_anom$is_high_percentile == TRUE, ], color = 'darkred', size = 2)

I have marked the 5% high and low percentiles with small red and blue dots and the outliers with bigger light red dots. You can shift a threshold of the percentile and interquartile distance as well (by changing the coefficient that equals 1.5 now).

#3 – The metric approach determines how far one observation is from the others in the space. Obviously, a typical observation is placed close to another, and the anomalous ones are farther. In this approach, the specific distance of the Mahalanobis works well for the business metrics analysis. A feature of the Mahalanobis distance approach different the from Euclidean one is that it takes into account the correlation between variables. From the anomaly detection point of view, this has the following effect: if for example the sessions from all channels synchronously grew twofold, then this approach can have the same anomaly estimation, as well as the case in which the number of sessions increased 1.5 times only from one channel.

In this case, observation is, for example, a day that is described by different metrics and their dimensions. Accordingly, we can look at these statistics from different angles. For example, whether the day was anomalous in terms of the structure of a certain metric, for instance, if the structure of traffic by the channels was typical. On the other hand, one can see whether the day was abnormal in terms of certain metrics, for example, the number of sessions and goals.

In addition, we need to apply a threshold of what distance will be used as an anomaly criterion. For this, we can use an exact value or combine it with the statistical approach but for distances this time. In the following example, I have analyzed the structure (dimensions) of sessions by dates and marked values that are in 95-100% percentile:

click to expand R code

##### 3 Metric approach ##### # Mahalanobis distance function maha_func <- function(x) { x <- x %>% select(-1) x <- x[, which( round(colMeans(x), 4) != 0 & apply(x, MARGIN = 2, FUN = sd) != 0) ] round(mahalanobis(x, colMeans(x), cov(x)), 2) } df_ses_maha <- df_all %>% # select the metrics select(-goals, -goals_per_session) %>% # casting dcast(., date ~ channel, value.var = 'sessions') %>% # remove total values select(-total) df_ses_maha[is.na(df_ses_maha)] <- 0 # adding Mahalanobis distances df_ses_maha$m_dist <- maha_func(df_ses_maha) df_ses_maha <- df_ses_maha %>% mutate(is_anomaly = ifelse(ecdf(m_dist)(m_dist) >= 0.95, TRUE, FALSE)) # visualization df_maha_plot <- df_ses_maha %>% select(-m_dist, -is_anomaly) %>% melt(., id.vars = 'date') df_maha_plot <- full_join(df_maha_plot, df_maha_plot, by = 'date') %>% left_join(., df_ses_maha %>% select(date, m_dist, is_anomaly), by = 'date') # color palette cols <- c("#4ab04a", "#eec73a", "#ffd73e", "#f05336", "#ce472e") mv <- max(df_maha_plot$m_dist) ggplot(df_maha_plot, aes(x = value.x, y = value.y, color = m_dist)) + theme_minimal() + facet_grid(variable.x ~ variable.y) + scale_color_gradientn(colors = cols, limits = c(min(df_maha_plot$m_dist), max(df_maha_plot$m_dist)), breaks = c(0, mv), labels = c("0", mv), guide = guide_colourbar(ticks = T, nbin = 50, barheight = .5, label = T, barwidth = 10)) + geom_point(aes(color = m_dist), size = 2, alpha = 0.4) + geom_text_repel(data = subset(df_maha_plot, is_anomaly == TRUE), aes(label = as.character(date)), fontface = 'bold', size = 2.5, alpha = 0.6, nudge_x = 200, direction = 'y', hjust = 1, segment.size = 0.2, max.iter = 10) + theme(legend.position = 'bottom', legend.direction = 'horizontal', panel.grid.major = element_blank())

As you can see on the chart, which is a set of intersections of all dimensions, the dates that were detected as anomalies are located farther in the space at most intersections.

#4 – Machine learning methods are also good ways of detecting anomalies but may require more attention to parameters tuning. In this article, I want to mention the Isolation Forest algorithm, which is a variation of Random Forest and its idea is the following: the algorithm creates random trees until each object is in a separate leaf and if there are outliers in the data, they will be isolated in the early stages (at a low depth of the tree). Then, for each observation, we calculate the mean of the depths of the leaves it falls into, and, based on this value, we decide whether or not it is an anomaly.

Again, as in the Metrics approach, we can estimate observations (dates in our example) in different ways and need to choose a threshold of an anomaly. I have used the same method as for the Metrics approach:

click to expand R code

##### 4 Isolation Forest ##### df_ses_if <- df_all %>% # select the metrics select(-goals, -goals_per_session) %>% # casting dcast(., date ~ channel, value.var = 'sessions') %>% # remove total values select(-total) df_ses_if[is.na(df_ses_if)] <- 0 # creating trees if_trees <- IsolationTrees(df_ses_if[, -1]) # evaluating anomaly score if_anom_score <- AnomalyScore(df_ses_if[, -1], if_trees) # adding anomaly score df_ses_if$anom_score <- round(if_anom_score$outF, 4) df_ses_if <- df_ses_if %>% mutate(is_anomaly = ifelse(ecdf(anom_score)(anom_score) >= 0.95, TRUE, FALSE)) # visualization df_if_plot <- df_ses_if %>% select(-anom_score, -is_anomaly) %>% melt(., id.vars = 'date') df_if_plot <- full_join(df_if_plot, df_if_plot, by = 'date') %>% left_join(., df_ses_if %>% select(date, anom_score, is_anomaly), by = 'date') # color palette cols <- c("#4ab04a", "#eec73a", "#ffd73e", "#f05336", "#ce472e") mv <- max(df_if_plot$anom_score) ggplot(df_if_plot, aes(x = value.x, y = value.y, color = anom_score)) + theme_minimal() + facet_grid(variable.x ~ variable.y) + scale_color_gradientn(colors = cols, limits = c(min(df_if_plot$anom_score), max(df_if_plot$anom_score)), breaks = c(0, mv), labels = c("0", mv), guide = guide_colourbar(ticks = T, nbin = 50, barheight = .5, label = T, barwidth = 10)) + geom_point(aes(color = anom_score), size = 2, alpha = 0.4) + geom_text_repel(data = subset(df_if_plot, is_anomaly == TRUE), aes(label = as.character(date)), fontface = 'bold', size = 2.5, alpha = 0.6, nudge_x = 200, direction = 'y', hjust = 1, segment.size = 0.2, max.iter = 10) + theme(legend.position = 'bottom', legend.direction = 'horizontal', panel.grid.major = element_blank())

The results are a bit different compared to the Metrics approach but almost the same.

In conclusion, I want to add a few thoughts that can be useful when you create your own system for detecting anomalies:

  • Usually, business changes over time and this is why we do all this. But changes are reflected both in the values of metrics and the dimensions by which these metrics are being tracked (for example, the advertising campaigns, landings, etc. can be changed/added/removed). In order to be realistic, I recommend working with a shifting historical window (or even several windows), for instance, use the data for the last 30, 60, 90, etc. days.
  • For quantitative indicators, the advice is not to feed them all together to an algorithm (e.g. Metric or Machine learning approaches) because, firstly, it can reduce the ability to identify an anomaly if only one dimension of a metric were affected. Secondly, it will be more difficult for us to understand why this day is considered anomalous and thus make a drill-down analysis.
  • Some observations can be identified as anomalies through several approaches. Thus, we can apply many different algorithms for determining what observations are anomalies by voting. This can be done, for example, using this package.

The detection of anomalies in business metrics helps the business “be alert” and thus respond in a timely manner to unexpected events. And the automatic Anomaly Detection system, in turn, allows you to significantly expand the range of the metrics and their dimensions and track many aspects of the business. Of course, there is a huge variety of approaches, methods, and algorithms for detecting anomalies, and thus this article is intended to familiarize you with some of them, but I hope this will help you take the first steps to detecting anomalies for your business.

The post Anomaly Detection for Business Metrics with R appeared first on AnalyzeCore by Sergey Bryl' – data is beautiful, data is a story.

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Hotfix for Microsoft R Open 3.5.0 on Linux

Wed, 06/13/2018 - 21:50

(This article was first published on Revolutions, and kindly contributed to R-bloggers)

On Monday, we learned about a serious issue with the installer for Microsoft R Open on Linux-based systems. (Thanks to Norbert Preining for reporting the problem.) The issue was that the installation and de-installation scripts would modify the system shell, and did not use the standard practices to create and restore symlinks for system applications.

The Microsoft R team developed a solution the problem with the help of some Debian experts at Microsoft, and last night issued a hotfix for Microsoft R Open 3.5.0 which is now available for download. With this fix, the MRO installer no longer relinks /bin/sh to /bin/bash, and instead uses dpkg-divert for Debian-based platforms and update-alternatives for RPM-based platforms. We will also request a discussion with the Debian maintainers of R to further review our installation process. Finally, with the next release — MRO 3.5.1, scheduled for August 9 — we will also include the setup code (including the installation scripts) in the MRO GitHub repository for everybody to inspect and give feedback on. 

You can find more details about the issue, the how it was resolved, and the processes we have put in place to make sure it doesn’t happen again in the blog post linked below.

Microsoft Machine Learning Server blog: How we are fixing our installer for Microsoft R Open on Linux

 

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Discrete or continuous modeling ?

Wed, 06/13/2018 - 21:29

(This article was first published on R-english – Freakonometrics, and kindly contributed to R-bloggers)

Tuesday, we got our conference “Insurance, Actuarial Science, Data & Models” and Dylan Possamaï gave a very interesting concluding talk. In the introduction, he came back briefly on a nice discussion we usually have in economics on the kind of model we should consider. It was about optimal control. In many applications, we start with a one period economy, then a two period economy, and pretend that we can extend it to period economy. And then, the continuous case can also be considered. A few years ago, I was working on sports game as an optimal effort startegy (within in a game – fixed time). It was with a discrete model, I was running simulations to get an efficient frontier, where coaches might say “ok, now we have enough (positive) difference, and we get closer to the end of the game, so we can ‘lower the effort’ i.e. top players can relax a little bit” (it was on basket-ball games). I asked a good friend of mine, Romuald, to help me on some technical parts of proofs, but he did not like so much my discrete-time model, and wanted to move to continuous time. And for now six years, we keep saying that someday we should get back to that paper….

My initial thoughts were that the difference was really “cultural”: you are either a continuous-time sort of guy, or a discrete-time one (or maybe none of the two, but that’s another problem). He works with stochastic processes, I work with time series. Of course, we can find connections, but most of the time, the techniques are very different. And tuesday, Dylan mentioned a very nice illustration that it’s not necessarily a cultural difference, and sometimes, it is great to move to continuous time. So I wanted to illustrate that idea.

Consider for instance the following curve.

1 2 3 vu = seq(0,1,length=601) vv = sin(vu*pi) plot(vu,vv,type="l",lwd=2)

The goal is to find the value of the maximum, numerically. And here, there are two (very) different strategies

  • the discrete one: we see a (finite) collection of points – for instance, the graph above is a collection of 601 points (connected with a straight line) – and in that case, we need a standard algorithm (in ) to get the value of the maximum
  • the continuous one: we see a function , and in that case, we use optimization routines

In the second case, use for instance

1 2 3 4 5 6 optim(0,function(x) -sin(pi*x)) $par [1] 0.5   $value [1] -1

For the first case, we can use the standard R function, and see how long it takes to use simulations to get an approximation of the maximum

1 2 3 4 5 library(microbenchmark) max_time = function(n) median(microbenchmark(max(sin(runif(n)*pi)))$time) vn = 10^(seq(1,6,length=21)) vt = Vectorize(max_time)(vn) plot(vn,vt/1e9,col="blue",pch=19,type="b",log="xy")

but of course, some home-made code can also be used

1 2 3 4 5 6 7 8 c_max = function(n=100){ x = sin(runif(n)*pi) y = x[1] for(i in 2:length(x)) { if(x[i] &gt; y) { y = x[i] }} return(y)} max_time=function(n) median(microbenchmark(c_max(n))$time) lines(vn,vt/1e9,type="b")

We can add that horizontal red line using

1 abline(h=median(microbenchmark(optim(.5,function(x) sin(pi*x)))$time)/1e9,lty=2,col="red")

So, indeed, it looks like computational time to find the maximum in a list of elements is linear in , i.e. . And R code is faster than home-made code. But also, interestingly, using continus time (based on analysis techniques) can be much faster. So, sometimes, considering continuous time models can be much easier to solve, from a numerical perspective.

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wrapr 1.5.0 available on CRAN

Wed, 06/13/2018 - 19:43

(This article was first published on R – Win-Vector Blog, and kindly contributed to R-bloggers)

The R package wrapr 1.5.0 is now available on CRAN.

wrapr includes a lot of tools for writing better R code:

I’ll be writing articles on a number of the new capabilities. For now I just leave you with the nifty operator coalesce notation.

Coalesce takes values from its arguments in left to right order taking the first non-NA value (if any available):

NA %?% 5 # [1] 5 1 %?% 5 # [1] 1 5 %?% NA # [1] 5

For vectors each position is calculated independently, and scalars are re-cycled to vector sizes. This allows fairly complicated coalesce strategies (such as take from first two vectors if possible, else write in zero) to be expressed very succinctly:

vec1 <- c(1, 2, NA, NA) vec2 <- c(10, NA, 20, NA) vec1 %?% vec2 %?% 0 # [1] 1 2 20 0 var vglnk = { key: '949efb41171ac6ec1bf7f206d57e90b8' }; (function(d, t) { var s = d.createElement(t); s.type = 'text/javascript'; s.async = true; s.src = '//cdn.viglink.com/api/vglnk.js'; var r = d.getElementsByTagName(t)[0]; r.parentNode.insertBefore(s, r); }(document, 'script'));

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2018-06 Rasterizing Chromatograms

Wed, 06/13/2018 - 05:03

(This article was first published on R – Stat Tech, and kindly contributed to R-bloggers)

This report describes an application of the ‘rasterize’ package for R. We rasterize (just) the line segments of two chromatograms in order to render one semi-transparently over the other. This also demonstrates, more generally, the value of having access to advanced graphical techniques within statistical graphics software.

Paul Murrell

Download

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Data + Art STEAM Project: Initial Results

Wed, 06/13/2018 - 03:55

(This article was first published on Little Miss Data, and kindly contributed to R-bloggers)

Big news

I’ve been incredibly fortunate as of late to work on an exciting STEAM project!  STEAM stands for science, technology, education, art and math.  It’s a term typically used in reference to education projects combining the subjects to creatively investigate a research area, solve a problem and teach students new skills. 

When I travelled back to Toronto in February, I met up with my good friend Katherine Lafranier.  Katherine, is a teacher to gifted grade 6 students at Forest Hill Junior and Senior Public School.  She was telling me how she just finished up a unit on data management.  Her students were already using Google Sheets for their analysis and graphing.  She saw my article on RAWGraphs.io and was considering unleashing them on that tool as well.  

  An idea is born

I was shocked at how early the students were working on data!  We started brainstorming about cool data projects and we came up with the concept of having the kids design a research project to explore a topic of their choice.  Their friends and schoolmates would be the subjects and they would gather data through surveys.  

  Where’s the Art?

If you’ve seen just about any other page on my blog, you will notice that I’m a sucker for beautiful data visualization!  To communicate their findings in the research project, we wanted to focus on effective data visualizations.  Oddly enough, right about the same time,  one of my instagram connections Letícia A. Pozza reached out to say that she is holding a data + art installation in Brazil.  She wanted to know if I had anything to display.   Of course the answer had to be YES, but we just needed to figure out how to mobilize this project to be applicable for an art installation.  I reached out to Katherine, and she had the idea of rolling up all of the data visualizations to a large mosaic style image of one of the graphs selected!

An example mockup of a word graph chart created with a series of graphs and images produced during the research.  The mockup was created with AndreaMosaic.

  Overview
  1. Students select a topic they are interested in researching.  They gather data through surveys with their schoolmates being the subjects.  Presentations, outlines and survey criteria are included in the materials below.  
  2. All data is submitted and consolidated into one csv file.
  3. Students and mentors use the data to create a large collection of images.  Image types include: data visualizations, hand drawn graphs, hand drawn images, photographs taken throughout the process, quotes from open text survey responses and other creative ideas.
  4. All images are rolled up into a large mosaic graphic that captures the subject area.  This will be the main display.  See the inset for an example of the mockup image.  
  5. A write up is completed to compliment the display. It outlines what the students learned during the investigation.  The write up will include a few images from the mosaic to highlight learnings.  

 

Materials

After creating the survey as a class, I sent back the final copy to Katherine.  She went through it with their students to get their final approval.  They sent it back with final comments and revisions.  

The steps are outlined in my github repo.  The overall outline for the project is available in pdf and word doc.  Additionally, the project introduction keynote and pdf files are available.  

If you have trouble downloading the file from github, go to the main page of the repo and select “Clone or Download” and then “Download Zip”.

    Project Topic

For our research project the students picked the subject: “Self-analysis:  Exploring student lifestyles and how it relates to their self-perception”

The final survey format is available here

  Early Results

We are currently in step 3 of the project as outlined in the “Overview” section above.  The students have created the survey, completed all surveying and we have a consolidated data set.  The students are working on image and graph creation. I’ve been fortunate enough to get a first pass at the data visualizations and have included some of the sample graphs below.

Graph Samples: Basic Graphs

It made sense to start the data visualizations with Google Sheets.  It is a free tool that the students already use. In my opinion it’s a solid free alternative to Excel that makes effective trend and total style graphs.

Technical Tips: If you have experience with Excel pivot tables and want to try Google Sheets, I’d suggest you start by going to the top navigation and select “Data” > “Pivot Table”.  Then use the right hand pop-out to add fields to the “Rows”, “Columns” and “Values” areas to create your summary table.   Note that “Values” can be aggregated by count, sum, avg.   When you have your summary table complete and you are ready to insert a chart select “Insert”  > “Chart” and change the “Chart Type” to your liking.  

 

Graph Samples: Pictorial Graphics

It can be very effective to use pictorial style graphs to create eye-catching data visualizations.  Pictorial graphics are often used to create infographics.  To create the graphs below I used Infogram

Technical Tips:  Infogram is a very straight forward tool.  To get started, you need your data already summarized.  For example, I needed to have the average screen times by introvert/extravert category already calculated for the graphs below.  You then find a graph type you like, replace the example data with your actual data, modify icons, colors etc and voila, you are done!

Average time spent on screens per week by social factors

Graph Samples: Complex Visualizations

I had to include graph creation with RAWGraphs.io   It is such a straight-forward and accessible tool to use without any need for coding!  The RAWGraph platform makes graphs accessible that are typically only available via Python, R, D3.

Technical Tips:  I have previously created a tutorial on RAWGraphs.io.  If you are interested in the tool, I’d suggest checking it out!

Graph Samples: Relationship visualization

Next up, I wanted to graph the relationship between our numerical variables: ScreenTime (hrs screen time per day), Sleep (hrs sleep a night), PhysActive (hrs physically active per week), HoursHomework (hrs of homework per week). 

One of the best ways to get a grip on relationships is to start with a basic correlation plot.  I chose R because it has a variety of really great options to display correlation plots.  My code is uploaded to the project repo here.  

When looking at the graph below, its very interesting to note that as screen time increases, sleep time decreases.  Of course correlation does not equal causation, but we should explore this further.  

Graph Samples: Relationships through scatterplots

Next, I wanted to graph scatterplots of these relationships.  I chose R again because of the easy and powerful ggplot2 plotting functionality.  My code is uploaded to the project repo here.  

I started out looking at various factors by gender and didn’t see any major differences.  

 

I continued by looking at the 1:1 relationships between numerical variables and grade.  In this discussion I believe that grade can be used as a proxy for age. I also added a regression line to see the trend of the variable relationships.  At first blush it looks like the time spent on homework increases with age.  Time spent sleeping decreases with age.  Time spent on physical activity decreases with age.  Finally, time spent on screens increases with age.  

I then looked at how screen time may be related to sleep time.  From the graph below, it would appear that as screen time increases, sleep time decreases.  But wait!  There may be a confounding factor here: age.  If you look above, sleep decreases with age and screen time increases with age.  So we isolate for age by plotting each age in their own graph.  Still, we see a similar trend that sleep time decreases with an increase in screen time.  Please keep in mind that we are just looking at trends here.  We would need more data and testing to more concretely declare this as fact.

 

Graph Samples: Additional Factor Visualizations

I continued the fun by exploring homework time and sleep by favorite subject.  Also I used a violin plot to look at the spectrum of sleep time by sociability factors (introvert/extravert).  Again, my code is uploaded to the project repo here.  

 

Graph Samples: Word Charts

Finally, I created some word plots.  The star word plot outlines the students desired future career.  The comment word plot outlines how the students view themselves.  The heart word plot outlines how the students like to spend their time.  

I created these plots with Tagxedo because I like the shapes can produce.  However, you could use Wordle or any other tool you have available to you.  They are all quite straight forward.  

  Call for Participation

This is the first pass at this project.  However, I have a number of contacts in the data scene that are interested in running another set of these projects possibly in coordination with other classrooms around the world.  If you are interested in participating, please contact me by filling out the form on my “Data for Good” page. 

  • Teachers, there is an opportunity to request your classrooms participation. 
  • Data folks, you can request to participate as mentors in the next project.  Also, if you are itching to take a crack at the current dataset, you can find it here.  Please feel free to send me any results and we may include them in the final project. 
  Thank you and Stay Tuned

We are not complete with our STEAM project yet!  The students need to create the images.   As a team, we need to produce our mosaic image, create the write up and select the highlight images.  We also have a surprise in store for how we are going to display the results from this project.  Thank you again for reading about our STEAM project. Stay tuned for more information!

 

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MOVIE BROWSER

Wed, 06/13/2018 - 03:48

(This article was first published on R – NYC Data Science Academy Blog, and kindly contributed to R-bloggers)

Movie Browser is here to help you discover new movies to watch, in a lot of different ways. You’ll be able to browse everything from new movies, Documentaries and TV shows, to the best movies in the 1970’s.
The app lets you see the Critics, IMDB and Audience score of all feature films, TV shows and documentaries.
The main motivation for this project was to have most of the Films, Tv Shows and documentaries all in one place with their reviews according to different genres.

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Monte Carlo Part Two

Wed, 06/13/2018 - 02:00

(This article was first published on R Views, and kindly contributed to R-bloggers)




























In a previous post, we reviewed how to set up and run a Monte Carlo (MC) simulation of future portfolio returns and growth of a dollar. Today, we will run that simulation many, many, times and then visualize the results.

Our ultimate goal is to build a Shiny app that allows an end user to build a custom portfolio, simulate returns, and visualize the results. If you just can’t wait, a link to the final Shiny app is available here.

This post builds off the work we did previously. I won’t go through the logic again, but the code for building a portfolio, calculating returns, mean and standard deviation of returns, and using them for a simulation is here:

library(tidyquant) library(tidyverse) library(timetk) library(broom) library(highcharter) symbols <- c("SPY","EFA", "IJS", "EEM","AGG") prices <- getSymbols(symbols, src = 'yahoo', from = "2012-12-31", to = "2017-12-31", auto.assign = TRUE, warnings = FALSE) %>% map(~Ad(get(.))) %>% reduce(merge) %>% `colnames<-`(symbols) w <- c(0.25, 0.25, 0.20, 0.20, 0.10) asset_returns_long <- prices %>% to.monthly(indexAt = "lastof", OHLC = FALSE) %>% tk_tbl(preserve_index = TRUE, rename_index = "date") %>% gather(asset, returns, -date) %>% group_by(asset) %>% mutate(returns = (log(returns) - log(lag(returns)))) %>% na.omit() portfolio_returns_tq_rebalanced_monthly <- asset_returns_long %>% tq_portfolio(assets_col = asset, returns_col = returns, weights = w, col_rename = "returns", rebalance_on = "months") mean_port_return <- mean(portfolio_returns_tq_rebalanced_monthly$returns) stddev_port_return <- sd(portfolio_returns_tq_rebalanced_monthly$returns) simulation_accum_1 <- function(init_value, N, mean, stdev) { tibble(c(init_value, 1 + rnorm(N, mean, stdev))) %>% `colnames<-`("returns") %>% mutate(growth = accumulate(returns, function(x, y) x * y)) %>% select(growth) }

That code allows us to run one simulation of the growth of a dollar over the next 10 years, with the simulation_accum_1() that we built for that purpose. Today, we will review how to run 51 simulations, though we could choose any number (and our Shiny application allows an end user to do just that).

First, we need an empty matrix with 51 columns, an initial value of $1, and intuitive column names.

We will use the rep() function to create 51 columns with a 1 as the value, and set_names() to name each column with the appropriate simulation number.

sims <- 51 starts <- rep(1, sims) %>% set_names(paste("sim", 1:sims, sep = ""))

Take a peek at starts to see what we just created, and how it can house our simulations.

head(starts) sim1 sim2 sim3 sim4 sim5 sim6 1 1 1 1 1 1 tail(starts) sim46 sim47 sim48 sim49 sim50 sim51 1 1 1 1 1 1

51 columns, with a value of 1 in one row. This is where we will store the results of the 51 simulations.

Now, we want to apply simulation_accum_1 to each of the 51 columns of the starts matrix, and we will do that using the map_dfc() function from the purrr package.

map_dfc() takes a vector – in this case, the columns of starts – and applies a function to it. By appending dfc() to the map_ function, we are asking the function to store each of its results as the column of a data frame (map_df() does the same thing, but stores results in the rows of a data frame). After running the code below, we will have a data frame with 51 columns, one for each of our simulations.

We also need to choose how many months to simulate (the N argument to our simulation function) and supply the distribution parameters as we did before. We do not supply the init_value argument because the init_value is 1, that same 1 that is already in the 51 columns.

monte_carlo_sim_51 <- map_dfc(starts, simulation_accum_1, N = 120, mean = mean_port_return, stdev = stddev_port_return) tail(monte_carlo_sim_51 %>% select(growth1, growth2, growth49, growth50), 3) # A tibble: 3 x 4 growth1 growth2 growth49 growth50 1 1.81 1.38 2.32 1.80 2 1.84 1.37 2.38 1.84 3 1.82 1.33 2.39 1.82

Have a look at the results. We now have 51 simulations of the growth of a dollar, and we simulated that growth over 120 months; however, the results are missing a piece that we need for visualization, namely a month column.

Let’s add that month column with mutate() and give it the same number of rows as our data frame. These are months out into the future. We will use mutate(month = seq(1:nrow(.))), and then clean up the column names. nrow() is equal to the number of rows in our object. If we were to change to 130 simulations, that would generate 130 rows, and nrow() would be equal to 130.

monte_carlo_sim_51 <- monte_carlo_sim_51 %>% mutate(month = seq(1:nrow(.))) %>% select(month, everything()) %>% `colnames<-`(c("month", names(starts))) %>% mutate_all(funs(round(., 2))) tail(monte_carlo_sim_51 %>% select(month, sim1, sim2, sim49, sim50), 3) # A tibble: 3 x 5 month sim1 sim2 sim49 sim50 1 119 2.16 1.81 1.46 2.32 2 120 2.28 1.84 1.46 2.38 3 121 2.26 1.82 1.46 2.39

We have accomplished our goal of running 51 simulations, and could head to data visualization now, but let’s explore an alternative method using the the rerun() function from purrr. As its name implies, this function will “rerun” another function, and we stipulate how many times to do that by setting .n = number of times to rerun. For example to run the simulation_accum_1 function 5 times, we would set the following:

monte_carlo_rerun_5 <- rerun(.n = 5, simulation_accum_1(1, 120, mean_port_return, stddev_port_return))

That returned a list of 5 data frames, or 5 simulations. We can look at the first few rows of each data frame by using map(..., head).

map(monte_carlo_rerun_5, head) [[1]] # A tibble: 6 x 1 growth 1 1 2 0.983 3 0.965 4 0.946 5 0.967 6 0.962 [[2]] # A tibble: 6 x 1 growth 1 1 2 0.980 3 0.975 4 0.964 5 0.969 6 0.914 [[3]] # A tibble: 6 x 1 growth 1 1 2 1.03 3 0.997 4 0.979 5 1.04 6 1.04 [[4]] # A tibble: 6 x 1 growth 1 1 2 0.974 3 0.962 4 0.943 5 0.942 6 0.963 [[5]] # A tibble: 6 x 1 growth 1 1 2 0.990 3 1.02 4 1.06 5 1.12 6 1.13

Let’s consolidate that list of data frames to one tibble. We start by collapsing to vectors with simplify_all(), then add nicer names with the names() function and finally coerce to tibble with as_tibble(). Let’s run it 51 times to match our previous results.

reruns <- 51 monte_carlo_rerun_51 <- rerun(.n = reruns, simulation_accum_1(1, 120, mean_port_return, stddev_port_return)) %>% simplify_all() %>% `names<-`(paste("sim", 1:reruns, sep = " ")) %>% as_tibble() %>% mutate(month = seq(1:nrow(.))) %>% select(month, everything()) tail(monte_carlo_rerun_51 %>% select(`sim 1`, `sim 2`, `sim 49`, `sim 50`), 3) # A tibble: 3 x 4 `sim 1` `sim 2` `sim 49` `sim 50` 1 1.99 1.97 3.66 2.20 2 2.00 1.86 3.68 2.25 3 2.02 1.95 3.78 2.18

Now we have two objects holding the results of 51 simulations, monte_carlo_rerun_51 and monte_carlo_sim_51.

Each has 51 columns of simulations and 1 column of months. Note that we have 121 rows because we started with an initial value of 1, and then simulated returns over 120 months.

Now let’s get to visualization with ggplot() and visualize the results in monte_carlo_sim_51. The same code flows for visualization would also apply to monte_carlo_rerun_51, but we will run them for only monte_carlo_sim_51 here.

We start with a chart of all 51 simulations, and assign a different color to each one by setting ggplot(aes(x = month, y = growth, color = sim)). ggplot() will automatically generate a legend for all 51 time series, but that gets quite crowded. We will suppress the legend with theme(legend.position = "none").

monte_carlo_sim_51 %>% gather(sim, growth, -month) %>% group_by(sim) %>% ggplot(aes(x = month, y = growth, color = sim)) + geom_line() + theme(legend.position="none")

We can check the minimum, maximum and median simulation with the summarise() function here.

sim_summary <- monte_carlo_sim_51 %>% gather(sim, growth, -month) %>% group_by(sim) %>% summarise(final = last(growth)) %>% summarise( max = max(final), min = min(final), median = median(final)) sim_summary # A tibble: 1 x 3 max min median 1 4.81 1.31 2.3

We can clean up our original visualization by including only the max, min and median that were just calculated.

monte_carlo_sim_51 %>% gather(sim, growth, -month) %>% group_by(sim) %>% filter( last(growth) == sim_summary$max || last(growth) == sim_summary$median || last(growth) == sim_summary$min) %>% ggplot(aes(x = month, y = growth)) + geom_line(aes(color = sim))

Now let’s port our results over to highcharter, but in a major departure from our usual code flow, we will pass a tidy tibble instead of an xts object.

Our first step is to convert the data from wide to long tidy format with the gather() function.

mc_gathered <- monte_carlo_sim_51 %>% gather(sim, growth, -month) %>% group_by(sim) head(mc_gathered) # A tibble: 6 x 3 # Groups: sim [1] month sim growth 1 1 sim1 1 2 2 sim1 0.99 3 3 sim1 1.01 4 4 sim1 1.06 5 5 sim1 1.08 6 6 sim1 1.1

We can now pass this tibble directly to the hchart() function, specify the type of chart as line, and then work with a similar grammar to ggplot(). The difference is we use hcaes, which stands for highcharter aesthetic, instead of aes.

# This takes a few seconds to run hchart(mc_gathered, type = 'line', hcaes(y = growth, x = month, group = sim)) %>% hc_title(text = "51 Simulations") %>% hc_xAxis(title = list(text = "months")) %>% hc_yAxis(title = list(text = "dollar growth"), labels = list(format = "${value}")) %>% hc_add_theme(hc_theme_flat()) %>% hc_exporting(enabled = TRUE) %>% hc_legend(enabled = FALSE)

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We just plotted 51 lines in highcharter using a tidy tibble. For tidy data fans out there, this is a big deal because we can stay in the grammar of the tidyverse but also use highcharter.

Very similar to what we did with ggplot, let’s isolate the maximum, minimum and median simulations and save them to an object called mc_max_med_min.

mc_max_med_min <- mc_gathered %>% filter( last(growth) == sim_summary$max || last(growth) == sim_summary$median || last(growth) == sim_summary$min) %>% group_by(sim)

Now we pass that filtered object to hchart().

hchart(mc_max_med_min, type = 'line', hcaes(y = growth, x = month, group = sim)) %>% hc_title(text = "Min, Max, Median Simulations") %>% hc_xAxis(title = list(text = "months")) %>% hc_yAxis(title = list(text = "dollar growth"), labels = list(format = "${value}")) %>% hc_add_theme(hc_theme_flat()) %>% hc_exporting(enabled = TRUE) %>% hc_legend(enabled = FALSE)

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That concludes our visualization of Monte Carlo simulations.

_____='https://rviews.rstudio.com/2018/06/13/monte-carlo-part-two/';

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Late anniversary edition redux: conditional vs marginal models for clustered data

Wed, 06/13/2018 - 02:00

(This article was first published on ouR data generation, and kindly contributed to R-bloggers)

This afternoon, I was looking over some simulations I plan to use in an upcoming lecture on multilevel models. I created these examples a while ago, before I started this blog. But since it was just about a year ago that I first wrote about this topic (and started the blog), I thought I’d post this now to mark the occasion.

The code below provides another way to visualize the difference between marginal and conditional logistic regression models for clustered data (see here for an earlier post that discusses in greater detail some of the key issues raised here.) The basic idea is that both models for a binary outcome are valid, but they provide estimates for different quantities.

The marginal model is estimated using a generalized estimating equation (GEE) model (here using function geeglm in package geepack). If the intervention is binary, the intervention effect (log-odds ratio) is interpreted as the average effect across all individuals regardless of the group or cluster they might belong to. (This estimate is sensitive to the relative sizes of the clusters.)

The conditional model is estimated using a random mixed effect generalized linear model (using function glmer in package lme4), and provides the log-odds ratio conditional on the cluster. (The estimate is not as sensitive to the relative sizes of the clusters since it is essentially providing a within-cluster effect.)

As the variation across clusters increases, so does the discrepancy between the conditional and marginal models. Using a generalized linear model that ignores clustering altogether will provide the correct (marginal) point estimate, but will underestimate the underlying variance (and standard errors) as long as there is between cluster variation. If there is no between cluster variation, the GLM model should be fine.

Simulation

To start, here is a function that uses simstudy to define and generate a data set of individuals that are clustered in groups. A key argument passed to this function is the across cluster variation.

library(lme4) library(geepack) library(broom) genFunc <- function(nClusters, effVar) { # define the cluster def1 <- defData(varname = "clustEff", formula = 0, variance = effVar, id = "cID") def1 <- defData(def1, varname = "nInd", formula = 40, dist = "noZeroPoisson") # define individual level data def2 <- defDataAdd(varname = "Y", formula = "-2 + 2*grp + clustEff", dist = "binary", link = "logit") # generate cluster level data dtC <- genData(nClusters, def1) dtC <- trtAssign(dtC, grpName = "grp") # generate individual level data dt <- genCluster(dtClust = dtC, cLevelVar = "cID", numIndsVar = "nInd", level1ID = "id") dt <- addColumns(def2, dt) return(dt) }

A plot of the average site level outcome from data generated with across site variance of 1 (on the log-odds scale) shows the treatment effect:

set.seed(123) dt <- genFunc(100, 1) dt ## cID grp clustEff nInd id Y ## 1: 1 0 -0.5604756 35 1 1 ## 2: 1 0 -0.5604756 35 2 0 ## 3: 1 0 -0.5604756 35 3 0 ## 4: 1 0 -0.5604756 35 4 0 ## 5: 1 0 -0.5604756 35 5 0 ## --- ## 3968: 100 1 -1.0264209 45 3968 0 ## 3969: 100 1 -1.0264209 45 3969 0 ## 3970: 100 1 -1.0264209 45 3970 1 ## 3971: 100 1 -1.0264209 45 3971 0 ## 3972: 100 1 -1.0264209 45 3972 0 dplot <- dt[, mean(Y), keyby = .(grp, cID)] davg <- dt[, mean(Y)] ggplot(data = dplot, aes(x=factor(grp), y = V1)) + geom_jitter(aes(color=factor(grp)), width = .10) + theme_ksg("grey95") + xlab("group") + ylab("mean(Y)") + theme(legend.position = "none") + ggtitle("Site level means by group") + scale_color_manual(values = c("#264e76", "#764e26"))

Model fits

First, the conditional model estimates a log-odds ratio of 1.89, close to the actual log-odds ratio of 2.0.

glmerFit <- glmer(Y ~ grp + (1 | cID), data = dt, family="binomial") tidy(glmerFit) ## term estimate std.error statistic p.value group ## 1 (Intercept) -1.8764913 0.1468104 -12.781729 2.074076e-37 fixed ## 2 grp 1.8936999 0.2010359 9.419711 4.523292e-21 fixed ## 3 sd_(Intercept).cID 0.9038166 NA NA NA cID

The marginal model that takes into account clustering yields an estimate of 1.63. This model is not wrong, just estimating a different quantity:

geeFit <- geeglm(Y ~ grp, family = binomial, data = dt, corstr = "exchangeable", id = dt$cID) tidy(geeFit) ## term estimate std.error statistic p.value ## 1 (Intercept) -1.620073 0.1303681 154.42809 0 ## 2 grp 1.628075 0.1740666 87.48182 0

The marginal model that ignores clustering also estimates a log-odds ratio, 1.67, but the standard error estimate is much smaller than in the previous model (0.076 vs. 0.174). We could say that this model is not appropriate given the clustering of individuals:

glmFit <- glm(Y ~ grp, data = dt, family="binomial") tidy(glmFit) ## term estimate std.error statistic p.value ## 1 (Intercept) -1.639743 0.0606130 -27.05267 3.553136e-161 ## 2 grp 1.668143 0.0755165 22.08978 3.963373e-108 Multiple replications

With multiple replications (in this case 100), we can see how each model performs under different across cluster variance assumptions. I have written two functions (that are shown at the end in the appendix) to generate multiple datasets and create a plot. The plot shows (1) the average point estimate across all the replications in black, (2) the true standard deviation of all the point estimates across all replications in blue, (3) the average estimate of the standard errors in orange.

In the first case, the variability across sites is highest. The discrepancy between the marginal and conditional models is relatively large, but both the GEE and mixed effects models estimate the standard errors correctly (the orange line overlaps perfectly with blue line). The generalized linear model, however, provides a biased estimate of the standard error – the orange line does not cover the blue line:

set.seed(235) res1.00 <- iterFunc(40, 1.00, 100) s1 <- sumFunc(res1.00) s1$p

When the across cluster variation is reduced, the discrepancy between the marginal and conditional models is reduced, as is the bias of standard error estimate for the GLM model:

res0.50 <- iterFunc(40, 0.50, 100) s2 <- sumFunc(res0.50) s2$p

Finally, when there is negligible variation across sites, the conditional and marginal models are pretty much one and the same. And even the GLM model that ignores clustering is unbiased (which makes sense, since there really is no clustering):

res0.05 <- iterFunc(40, 0.05, 100) s3 <- sumFunc(res0.05) s3$p

Appendix

Here are the two functions that generated the the replications and created the plots shown above.

iterFunc <- function(nClusters, effVar, iters = 250) { results <- list() for (i in 1:iters) { dt <- genFunc(nClusters, effVar) glmerFit <- glmer(Y ~ grp + (1 | cID), data = dt, family="binomial") glmFit <- glm(Y ~ grp, data = dt, family="binomial") geeFit <- geeglm(Y ~ grp, family = binomial, data = dt, corstr = "exchangeable", id = dt$cID) res <- unlist(c(coef(summary(glmerFit))[2,1:2], coef(summary(glmFit))[2,1:2], as.vector(coef(summary(geeFit))[2,1:2]))) results[[i]] <- data.table(t(res)) } return(rbindlist(results)) } sumFunc <- function(dtRes, precision = 2) { setnames(dtRes, c("estGlmer", "sdGlmer", "estGlm","sdGlm", "estGEE", "sdGEE")) meanEst <- round(apply(dtRes[, c(1, 3, 5)], 2, mean), precision) estSd <- round(sqrt(apply(dtRes[, c(2, 4, 5)]^2, 2, mean)), precision) sdEst <- round(apply(dtRes[, c(1, 3, 5)], 2, sd), precision) x <- data.table(rbind(c(meanEst[1], estSd[1], sdEst[1]), c(meanEst[2], estSd[2], sdEst[2]), c(meanEst[3], estSd[3], sdEst[3]) )) setnames(x, c("estMean","estSD","sd")) x[, method := c("glmer","glm","gee")] p <- ggplot(data = x, aes(x = method, y = estMean)) + geom_errorbar(aes(ymin = estMean - sd, ymax = estMean + sd), width = 0.1, color = "#2329fe", size = 1) + geom_errorbar(aes(ymin = estMean - estSD, ymax = estMean + estSD), width = 0.0, color = "#fe8b23", size = 1.5) + geom_point(size = 2) + ylim(1,2.75) + theme_ksg("grey95") + geom_hline(yintercept = 2, lty = 3, color = "grey50") + theme(axis.title.x = element_blank()) + ylab("Treatment effect") return(list(mean=meanEst, sd=sdEst, p=p)) } var vglnk = { key: '949efb41171ac6ec1bf7f206d57e90b8' }; (function(d, t) { var s = d.createElement(t); s.type = 'text/javascript'; s.async = true; s.src = '//cdn.viglink.com/api/vglnk.js'; var r = d.getElementsByTagName(t)[0]; r.parentNode.insertBefore(s, r); }(document, 'script'));

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Beautiful Visualizations in R

Tue, 06/12/2018 - 19:24

(This article was first published on Deeply Trivial, and kindly contributed to R-bloggers)

I recently discovered the R Graph Gallery, where users can share the beautiful visualizations they’ve created using R and its various libraries (especially ggplot2). One of my favorite parts about this gallery is a section called Art From Data, in which users create works of art, sometimes with real data, and sometimes with a random number generator and a little imagination.

Last night, I completed a DataCamp project to learn how to draw flowers in R and ggplot2. Based on that, I created this little yellow flower:

Not only was the flower fun to create, it made me think about the data and how it would appear spatially. As I try to create new and more complex images, I have to keep building on and challenging those skills. It’s a good exercise to get you thinking about data.

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