Chapter 5 Linear modeling theory

So far, we have been studying linear models and linear mixed models rather informally. This approach is good enough for a first-pass at linear modeling. However, in order to fully understand the underlying machinery of linear models, the matrix formulation of the linear model is extremely important and useful. There is a price to be paid, however: one has to reactivate one’s knowledge of matrix algebra, or one has to put in some work into reviewing elementary matrix theory. Fortunately, reviewing these concepts is not too difficult. We begin this chapter with a quick review of some basic concepts in matrix algebra, and then apply them to linear modeling. One very useful set of online lectures on the basic ideas behind linear algebra is the short set of videos by 3Blue1Brown: https://youtu.be/kjBOesZCoqc. You should look at these videos before reading the next section, if you have never encountered the basic concepts behind matrix algebra.