In most (observational) research papers you read, you will probably run into a correlation matrix. Often it looks something like this:

In Social Sciences, like Psychology, researchers like to denote the statistical significance levels of the correlation coefficients, often using asterisks (i.e., *). Then the table will look more like this:

Regardless of my personal preferences and opinions, I had to make many of these tables for the scientific (non-)publications of my Ph.D..

I remember that, when I first started using R, I found it quite difficult to generate these correlation matrices automatically.

Yes, there is the cor function, but it does not include significance levels.

Then there the (in)famous Hmisc package, with its rcorr function. But this tool provides a whole new range of issues.

What’s this storage.mode, and what are we trying to coerce again?

Soon you figure out that Hmisc::rcorr only takes in matrices (thus with only numeric values). Hurray, now you can run a correlation analysis on your dataframe, you think…

Yet, the output is all but publication-ready!

You wanted one correlation matrix, but now you have two… Double the trouble?

To spare future scholars the struggle of the early day R programming, I would like to share my custom functioncorrelation_matrix.

My correlation_matrix takes in a dataframe, selects only the numeric (and boolean/logical) columns, calculates the correlation coefficients and p-values, and outputs a fully formatted publication-ready correlation matrix!

For instance, you can use only 2 decimals. You can focus on the lower triangle (as the lower and upper triangle values are identical). And you can drop the diagonal values:

Or maybe you are interested in a different type of correlation coefficients, and not so much in significance levels:

For other formatting options, do have a look at the source code below.

Now, to make matters even more easy, I wrote a second function (save_correlation_matrix) to directly save any created correlation matrices:

Once you open your new correlation matrix file in Excel, it is immediately ready to be copy-pasted into Word!

If you are looking for ways to visualizeyour correlations do have a look at the packages corrr and corrplot.

I hope my functions are of help to you!

Do reach out if you get to use them in any of your research papers!

I would be super interested and feel honored.

correlation_matrix

#' correlation_matrix
#' Creates a publication-ready / formatted correlation matrix, using `Hmisc::rcorr` in the backend.
#'
#' @param df dataframe; containing numeric and/or logical columns to calculate correlations for
#' @param type character; specifies the type of correlations to compute; gets passed to `Hmisc::rcorr`; options are `"pearson"` or `"spearman"`; defaults to `"pearson"`
#' @param digits integer/double; number of decimals to show in the correlation matrix; gets passed to `formatC`; defaults to `3`
#' @param decimal.mark character; which decimal.mark to use; gets passed to `formatC`; defaults to `.`
#' @param use character; which part of the correlation matrix to display; options are `"all"`, `"upper"`, `"lower"`; defaults to `"all"`
#' @param show_significance boolean; whether to add `*` to represent the significance levels for the correlations; defaults to `TRUE`
#' @param replace_diagonal boolean; whether to replace the correlations on the diagonal; defaults to `FALSE`
#' @param replacement character; what to replace the diagonal and/or upper/lower triangles with; defaults to `""` (empty string)
#'
#' @return a correlation matrix
#' @export
#'
#' @examples
#' `correlation_matrix(iris)`
#' `correlation_matrix(mtcars)`
correlation_matrix <- function(df,
type = "pearson",
digits = 3,
decimal.mark = ".",
use = "all",
show_significance = TRUE,
replace_diagonal = FALSE,
replacement = ""){
# check arguments
stopifnot({
is.numeric(digits)
digits >= 0
use %in% c("all", "upper", "lower")
is.logical(replace_diagonal)
is.logical(show_significance)
is.character(replacement)
})
# we need the Hmisc package for this
require(Hmisc)
# retain only numeric and boolean columns
isNumericOrBoolean = vapply(df, function(x) is.numeric(x) | is.logical(x), logical(1))
if (sum(!isNumericOrBoolean) > 0) {
cat('Dropping non-numeric/-boolean column(s):', paste(names(isNumericOrBoolean)[!isNumericOrBoolean], collapse = ', '), '\n\n')
}
df = df[isNumericOrBoolean]
# transform input data frame to matrix
x <- as.matrix(df)
# run correlation analysis using Hmisc package
correlation_matrix <- Hmisc::rcorr(x, type = type)
R <- correlation_matrix$r # Matrix of correlation coeficients
p <- correlation_matrix$P # Matrix of p-value
# transform correlations to specific character format
Rformatted = formatC(R, format = 'f', digits = digits, decimal.mark = decimal.mark)
# if there are any negative numbers, we want to put a space before the positives to align all
if (sum(!is.na(R) & R < 0) > 0) {
Rformatted = ifelse(!is.na(R) & R > 0, paste0(" ", Rformatted), Rformatted)
}
# add significance levels if desired
if (show_significance) {
# define notions for significance levels; spacing is important.
stars <- ifelse(is.na(p), "", ifelse(p < .001, "***", ifelse(p < .01, "**", ifelse(p < .05, "*", ""))))
Rformatted = paste0(Rformatted, stars)
}
# make all character strings equally long
max_length = max(nchar(Rformatted))
Rformatted = vapply(Rformatted, function(x) {
current_length = nchar(x)
difference = max_length - current_length
return(paste0(x, paste(rep(" ", difference), collapse = ''), sep = ''))
}, FUN.VALUE = character(1))
# build a new matrix that includes the formatted correlations and their significance stars
Rnew <- matrix(Rformatted, ncol = ncol(x))
rownames(Rnew) <- colnames(Rnew) <- colnames(x)
# replace undesired values
if (use == 'upper') {
Rnew[lower.tri(Rnew, diag = replace_diagonal)] <- replacement
} else if (use == 'lower') {
Rnew[upper.tri(Rnew, diag = replace_diagonal)] <- replacement
} else if (replace_diagonal) {
diag(Rnew) <- replacement
}
return(Rnew)
}

save_correlation_matrix

#' save_correlation_matrix
#' Creates and save to file a fully formatted correlation matrix, using `correlation_matrix` and `Hmisc::rcorr` in the backend
#' @param df dataframe; passed to `correlation_matrix`
#' @param filename either a character string naming a file or a connection open for writing. "" indicates output to the console; passed to `write.csv`
#' @param ... any other arguments passed to `correlation_matrix`
#'
#' @return NULL
#'
#' @examples
#' `save_correlation_matrix(df = iris, filename = 'iris-correlation-matrix.csv')`
#' `save_correlation_matrix(df = mtcars, filename = 'mtcars-correlation-matrix.csv', digits = 3, use = 'lower')`
save_correlation_matrix = function(df, filename, ...) {
return(write.csv2(correlation_matrix(df, ...), file = filename))
}

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This blog highlights a recent PNAS paper in which 457 data scientists and academic scholars were challenged use machine learning to predict life outcomes using a rich dataset.

Yet, I can not summarize the result better than this tweet by the author of the paper:

Over 750 scientific papers have used the Fragile Families dataset.

The dataset is famous for its richness of cohort (survey) data on the included families’ lives and their childrens’ upbringings. It includes a whopping 12.942 variables!!

Some of these variables reflect interesting life outcomes of the included families.

For instance, the childrens’ grade point averages (GPA) and grit, but also whether the family was ever evicted or experienced hardship, or whether their primary caregiver had received job training or was laid off at work.

You can read more about the exact data contents in the paper’s appendix.

Now Matthew and his co-authors shared this enormous dataset with over 160 teams consisting of 457 academics researchers and data scientists alike. Each of them well versed in statistics and predictive modelling.

These data scientists were challenged with this task: by all means possible, make the most predictive model for the six life outcomes (i.e., GPA, conviction, etc).

The scientists could use all the Fragile Families data, and any algorithm they liked, and their final model and its predictions would be compared against the actual life outcomes in a holdout sample.

According to the paper, many of these teams used machine-learning methods that are not typically used in social science research and that explicitly seek to maximize predictive accuracy.

Now, here’s the summary again:

If hundreds of [data] scientists created predictive algorithms with high-quality data, how well would the best predict life outcomes?

Not very well.

@msalganik

Even the best among the 160 teams’ predictions showed disappointing resemblance of the actual life outcomes. None of the trained models/algorithms achieved an R-squared of over 0.25.

Here’s that same plot again, but from the original publication and with more detail:

Wondering what these best R-squared of around 0.20 look like? Here’s the disappointg reality of plot C enlarged: the actual TRUE GPA’s on the x-axis, plotted against the best team’s predicted GPA’s on the y-axis.

Sure, there’s some relationship, with higher actual scores getting higher (average) predictions. But it ain’t much.

Moreover, there’s very little variation in the predictions. They all clump together between the range of about 2.1 and 3.8… that’s not really setting apart the geniuses from the less bright!

Matthew sums up the implications quite nicely in one of his tweets:

For policymakers deploying predictive algorithms in high-stakes decisions, our result is a reminder of a basic fact: one should not assume that algorithms predict well. That must be demonstrated with transparent, empirical evidence.

According to Matthew this “collective failure of 160 teams” is hard to ignore. And it failure highlights the understanding vs. predicting paradox: these data have been used to generate knowledge on how the world works in over 750 papers, yet few checked to see whether these same data and the scientific models would be useful to predict the life outcomes we’re trying to understand.

I was super excited to read this paper and I love the approach. It is actually quite closely linked to a series of papers I have been working on with Brian Spisak and Brian Doornenbal on trying to predict which people will emerge as organizational leaders. (hint: we could not really, at least not based on their personality)

Apparently, others were as excited as I am about this paper, as Filiz Garip already published a commentary paper on this research piece. Unfortunately, it’s behind a paywall so I haven’t read it yet.

Moreover, if you want to learn more about the approaches the 160 data science teams took in modelling these life outcomes, here are twelve papers in which some teams share their attempts.

Very curious to hear what you think of the paper and its implications. You can access it here, and I’d love to read your comments below.

Google Brain researchers published this amazing paper, with accompanying GIF where they show the true power of AutoML.

AutoML stands for automated machine learning, and basically refers to an algorithm autonomously building the best machine learning model for a given problem.

This task of selecting the best ML model is difficult as it is. There are many different ML algorithms to choose from, and each of these has many different settings ([hyper]parameters) you can change to optimalize the model’s predictions.

For instance, let’s look at one specific ML algorithm: the neural network. Not only can we try out millions of different neural network architectures (ways in which the nodes and lyers of a network are connected), but each of these we can test with different loss functions, learning rates, dropout rates, et cetera. And this is only one algorithm!

In their new paper, the Google Brain scholars display how they managed to automatically discover complete machine learning algorithms just using basic mathematical operations as building blocks. Using evolutionary principles, they have developed an AutoML framework that tailors its own algorithms and architectures to best fit the data and problem at hand.

This is AI research at its finest, and the results are truly remarkable!

Both in science and business, we often experience difficulties collecting enough data to test our hypotheses, either because target groups are small or hard to access, or because data collection entails prohibitive costs.

Such obstacles may result in data sets that are too small for the complexity of the statistical model needed to answer the questions we’re really interested in.

This unique book provides guidelines and tools for implementing solutions to issues that arise in small sample studies. Each chapter illustrates statistical methods that allow researchers and analysts to apply the optimal statistical model for their research question when the sample is too small.

This book will enable anyone working with data to test their hypotheses even when the statistical model required for answering their questions are too complex for the sample sizes they can collect. The covered statistical models range from the estimation of a population mean to models with latent variables and nested observations, and solutions include both classical and Bayesian methods. All proposed solutions are described in steps researchers can implement with their own data and are accompanied with annotated syntax in R.

I came across this opinionated though informed commentary by Vinay Prasad on the recent Nature article where Google’s machine learning experts trained models to predict whether scans of patients’ breasts (mammogram’s) show cancerous cells or not.

Vinay Prasad [official bio] is a practicing hematologist-oncologist and Associate Professor of Medicine at Oregon Health and Science University. So he knows what he’s talking about.

He argues that “cancer screening is the LAST thing you should pick FIRST to work on with AI”. Which is an interesting statement in and of itself.

Regardless of my personal opinion on the topic, I found the paper, Vinay’s commentary, and the broader discussion on twitter very interesting and educational to read. I feel it shows how important it is to know the context in which you are applying machine learning. What tremendous value it provides to have domain experts in the same team as the data and machine learning experts.