## ABSTRACT

One of the limitations of cross-sectional analyses is that they are not well suited to studying processes that are assumed to be developmental. Longitudinal analysis represents a rapidly growing application of basic multilevel-modeling techniques. This chapter first briefly outlines some of the limitations of previous approaches used to examine longitudinal data (e.g., repeated-measures ANOVA). It then introduces the random-effects approach for analyzing changes within individuals and groups using several extended examples using IBM SPSS Mixed. The random-effects multilevel approach uses repeated observations nested within individuals defined at level 1 with differences between individuals defined at level 2. The researcher can specify initial status intercepts and time-related changes as random effects that vary between individuals. This basic two-level formulation also facilitates the specification of models with time-varying (within subjects) covariates and time-invariant (between subjects) covariates. The random-effects approach is appropriate when we assume the units in the analysis are part of a larger population. We also assume that their particular means may form the distribution of a random variable, and that we have the essential covariates available to model differences between subjects.