Statistics: An Introduction Using R, 2nd Edition

9Analysis of Covariance

Analysis of covariance (ANCOVA) involves a combination of regression and analysis of variance. The response variable is continuous, and there is at least one continuous explanatory variable and at least one categorical explanatory variable. Typically, the maximal model involves estimating a slope and an intercept (the regression part of the exercise) for each level of the categorical variable(s) (the ANOVA part of the exercise). Let us take a concrete example. Suppose we are modelling weight (the response variable) as a function of sex and age. Sex is a factor with two levels (male and female) and age is a continuous variable. The maximal model therefore has four parameters: two slopes (a slope for males and a slope for females) and two intercepts (one for males and one for females) like this:

Model simplification is an essential part of ANCOVA, because the principle of parsimony requires that we keep as few parameters in the model as possible.

There are at least six possible models in this case, and the process of model simplification begins by asking whether we need all four parameters (top left). Perhaps we could make do with two intercepts and ...