3.7 Summary

This chapter began by drawing a connection between the t-test and linear models; one important insight was that the paired t-test is identical to the linear mixed model with varying intercepts (assuming aggregated data). We learned about two kinds of contrast coding, treatment and sum contrasts, and we encountered the log transformation in the context of reading time data. Then, three types of increasingly complex linear mixed models were introduced, culminating in the model with varying intercepts and varying slopes both subjects and items, with correlation parameters estimated for the varying intercepts and slopes. The final topic covered in this chapter was about shrinkage in linear mixed models; an example analysis was used to show that one of the great advantages of the linear mixed model is that when data from an individual subject (or item) are sparse, or when a subject/item exhibits unusual behavior, the model conservatively shrinks that subject/item’s estimates towards the grand mean estimates (the fixed intercept and slope estimates), a phenomeon known as “borrowing strength from the mean”.