rmcorrShiny: A web and standalone application for repeated measures correlation

Introduction

The most common techniques for calculating the correlation between two variables (e.g., the Pearson correlation coefficient) assume that each pair of data points arises from an independent observation. Take, for example, a study that calculates the correlation between age and the volume of a specific brain region for a sample of people. In this example, each individual contributes a data point consisting of a brain volume and an age. However, it is not uncommon for studies to use repeated measures designs, such as a study by Raz et al.¹ that collected the brain region volume and age at two different time points. Each participant in this study contributed two (repeated) data points of paired measures. Repeated measures of the same individual are no longer independent observations and should not be analyzed as such. Erroneously modeling repeated measures data as independent observations is surprisingly prevalent in published research, even though such results will generally be misleading.^2-4 A common way to resolve this problem is to use aggregated data: first taking an average of the repeated measures data of each person so that every individual again contributes a single paired data point, and then calculating the correlation from these averages (between-participants). Another possibility is to use separate models to analyze each paired data point, removing the dependency. For example, the study by Raz et al.¹ computed separate correlations between brain region volume and age at each of the two time points.

Instead of aggregation or separate models, an alternative solution is to calculate the repeated measures correlation,^5-7 which assesses the common intra-individual (within-participants) association for paired repeated measures data. The repeated measures correlation technique is conceptually similar to a null multilevel model, with a common (fixed effect) slope but varying (random effect) intercept for each individual. It is calculated using a form of ANCOVA, and thus shares the same statistical assumptions as ANCOVA, with the exception of independence of errors. Using the repeated measures correlation has multiple potential benefits. It is simpler and more straightforward to implement than a multilevel model, with the potential for much greater statistical power than aggregation. In addition, repeated measures correlation can provide insights into patterns within individuals that may be obscured by aggregation or use of separate models (see, for example, the use case described below and illustrated in Figure 2).⁵

We previously developed the rmcorr package⁸ in R⁹ to make the repeated measures correlation technique widely available for researchers; it has since also been adapted as a function in the Pingouin statistics package¹⁰ for Python. However, the use of both of these packages requires some facility with programming languages, which may limit accessibility.

Methods

Implementation

Here we introduce rmcorrShiny, a Shiny¹¹ app, which provides an intuitive graphical interface for computing and plotting the repeated measures correlation. An example of the interface is shown in Figure 1.

Figure 1. Graphical interface for rmcorrShiny.

The interface consists of two panels, corresponding roughly to input (left) and output (right), with each containing multiple subpanels or tabs. The left panel has tabs for Input: uploading data or using sample data, Data Options: selecting variables for analysis, and Plot Options: customizing labels and plot appearance. The right panel has tabs for Results: statistical output from rmcorr, Plot: corresponding visualization of the rmcorr results, R code: the custom R code generating the analysis and plot for the selected data/options, Processed Data: summary statistics on data and raw viewer, Download: buttons to download the plot and generated R code, and About: information about the app.

The primary features of rmcorrShiny include:

• • The ability to import data in a variety of different file formats or to use one of four included sample datasets, described below. Missing observations in datasets are ignored using listwise deletion.

• • Options for bootstrapping the confidence interval (CI) for the rmcorr effect size.

• • The display of raw data and the output from rmcorr as well as formatted output for reporting scientific results.

• • Multiple options to generate and customize rmcorr plots, making use of the ggplot2 package^12,13 and palettes from the RColorBrewer¹⁴ and pals¹⁵ packages.

• • Customized R code generated using the data and options chosen by the user that can be directly pasted and executed in R to produce the same output as in rmcorrShiny, or as a starting point for additional customization in R.

• • The ability to download plots (in multiple file formats) or a .zip file of all output.

Note that many features in rmcorrShiny, including the panel interface, were based on modifications of code from the Raincloud-shiny app.¹⁶

devtools::install_github("lmarusich/rmcorrShiny")
library(rmcorrShiny)
rmcorrShiny::rmcorrShiny()

Use case

As a use case, we use rmcorrShiny to compute and plot the repeated measures correlation of raz2005¹, one of the four included sample datasets. The right panel of Figure 2 shows the rmcorr plot for this data. Because a variety of patterns in data can produce similar or even identical statistical results for rmcorr, as well as other models, we highly recommend visualization to aid in interpreting results. In Figure 2, the x-axis is age and the y-axis is volume of a brain area, the cerebellar hemisphere. Each participant, plotted in a different color, contributes two paired data points representing two assessments of age and brain volume. Paired age and brain volume were measured twice per participant about five years apart. The corresponding lines depict the repeated measures correlation model. Note the large negative slope and close fit of the lines to many of the data points. This shows a strong pattern of a common decrease in the volume of this brain area over time, across different ages. The lower left corner of the plot shows the effect size for rmcorr and its p-value.

Figure 2. Plot options and rmcorr plot of sample neuroscience dataset raz2005.¹

As mentioned previously, the pattern of results may vary, depending on whether the analysis is within- or between-individuals.^17,18 This can be observed in the current example; when the raz2005 dataset is analyzed using aggregation or separate models (between-individual analyses), the magnitude of the negative association is diminished in comparison to rmcorr (within-individual analysis; see Figure 5 in Bakdash & Marusich⁵).

Limitations

rmcorrShiny has the advantage of making the useful and already fairly simple-to-use rmcorr technique even more accessible and easy to implement and interpret. However, its limitations are the same as rmcorr’s: it does not have all of the capabilities of multilevel modeling and thus it is not a replacement. We recommend using multilevel modeling if: there are more than two outcome variables and/or predictors of interest, data have more than two levels (e.g., academic performance for students [Level 1] nested within classrooms [Level 2] nested within schools [Level 3]), simultaneous modeling of within- and between-participants is needed, visual patterns suggest varying slopes by individual and/or non-linear associations, or time needs to be explicitly included in the model (i.e., modeling change over time as a separate variable; note in Figure 2 age is a measure of time, but it is not a separate variable). For more information about multilevel modeling, see Aarts et al.² and the About tab in rmcorrShiny.

When running the app in the browser, users are limited to a maximum file size of 30 MB when uploading data. However, when running the app locally it should be possible to load larger files.

Conclusion

This paper demonstrates the rmcorrShiny app for graphing and analyzing paired, repeated measures data without requiring programming knowledge. By increasing the accessibility of the rmcorr technique, we aim to bolster the researcher's toolbox by providing a simple but powerful tool for examining associations present at the within-subject level in a way that does not violate independence assumptions or require use of separate models or data aggregation. In particular, this app may be useful for visualization and analysis of a common linear pattern across participants and could be an informative precursor complementing multilevel modeling.

Data availability

The rmcorrShiny app contains sample datasets from four previously published papers.

The csv files for datasets can be directly downloaded from Github (https://github.com/lmarusich/rmcorrShiny/tree/master/inst/shiny).

Software availability