Mixed-Effects Regression Modeling

In this chapter, mixed-effects regression modeling is introduced, mostly using alternation modeling as an example. It is one option to deal with cases where observations vary by groups (such as speakers, registers, lemmas) by introducing so-called random effects into the model specification. It is stressed that using a categorical variable as a random effect is just an alternative to using it as a normal fixed effect in a Generalised Linear Model (GLM) as introduced in Chap. 21, but that the two options have different mathematical advantages and disadvantages. Simple random intercepts are introduced, which capture per-group tendencies. However, random slopes (for situations where fixed effects vary per group) and multilevel models (for situations where group-wise tendencies can be predicted from other variables, for example when lemma frequency is useful to predict lemma-specific tendencies) are also introduced. Criteria for including random effects in models and for evaluating the model fit (for example through pseudo-coefficients of determination) are discussed. The demonstration in R uses the popular lme4 package.