Multilevel models in psychometrics

This chapter provides models for repeated measures and multivariate data. It also introduces structural equation models and provides a description of simple multilevel models for data from populations with a two-level hierarchical structure. An analysis of variance (ANOVA) or fixed effects model is a way of allowing for school effects, which involves explanatory variables as a set of dummy variables that indicate the school to which a student belongs. While ANOVA can also be used to compare any number of schools, the random effects approach has a number of advantages over fixed effects models. First, if there are J schools to be compared, then J−1 parameters are required to capture school effects, and therefore, if J is large, a large number of parameters need to be estimated. Second, the origins of ANOVA lie in experimental design where there are typically a small number of groups under comparison and all groups of interest are sampled. In a fixed effects model, the effects of level 2 explanatory variables cannot be separately estimated.