(This article was originally published at Statistical Modeling, Causal Inference, and Social Science, and syndicated at StatsBlogs.)

Anouschka Foltz writes:

One of my students has some data, and there is an issue with multiple comparisons. While trying to find out how to best deal with the issue, I came across your article with Martin Lindquist, “Correlations and Multiple Comparisons in Functional Imaging: A Statistical Perspective.” And while my student’s work does not involve functional imaging, I thought that your article may present a solution for our problem.

My student is interested in the relationship between vocabulary size and different vocabulary learning strategies (VLS). He has measured each participant’s approximate vocabulary size with a standardized test (scores between 0 and 10000) and asked each participant how frequently they use each of 37 VLS on a scale from 1 through 5. The 37 VLS fall into five different groups (cognitive, memory, social etc.). He is interested in which VLS correlate with or predict vocabulary size. To see which VSL correlate with vocabulary size, we could run 37 separate correlation analyses, but then we run into the problem that we are doing multiple comparisons and the issue of false positives that goes along with that.

Do you think a multilevel Bayesian approach that uses partial pooling, as you suggest in your paper for functional imaging date, would be appropriate in our case? If so, would you be able to provide me with some more information as to how I can actually run such an analysis? I am working in R, and any information as to which packages and functions would be appropriate for the analysis would be really helpful. I came across the brms package for Advanced Bayesian Multilevel Modeling, but I have not worked with this particular package before and I am not sure if this is exactly what I need.

My reply:

I do think a multilevel Bayesian approach would make sense. I’ve never worked on this particular problem. So I am posting it here on blog on the hope that someone might have a response. This seems like the exact sort of problem where we’d fit a multilevel model rather than running 37 separate analyses!

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