6 Can the regularization in mixed models be problematic?

Can we use conditional modes (BLUPs) in models? Does regularization hurt us? How does the two-stage summary statistics approach measure up to the standard mixed model? The previous videos illustrated what regularization within the mixed models looked like through conditional mode estimates (some call these BLUPs). When I explained regularization to my friend, she immediately pointed out that her patient groups are much smaller and often have more missing data and she wondered if the regularization could hurt her and whether the two stage summary statistics approach was better. Here I look at this question in the case of a two-sample t-test. Spoiler: Mixed Models will work great. See when the two stage summary statistics approach (using OLS ...aka linear regression at both stages) and pseudo two-stage summary statistics approaches using mixed model conditional modes perform (spoiler, this is a bad idea...don't do it please). *NEW* (12/31/2020) Bookdown version of R materials. This video's chapter can be found here: https://jmumford.github.io/MixedModelSeries/v6-model-strategy-comparison-group-differences.html