ABSTRACT
Random effects growth models provide a powerful and flexible statistical tool to behavioral researchers for the study of individual differences in stability and change over time. Within the hierarchical linear modeling (HLM) framework, the functional form of the relationship between the repeated measures and time is specified in the level 1 model. Individual variability in initial levels and in rates of change may then be modeled as a function of one or more predictor variables specified in the level 2 model. In growth models, the inclusion of a main–effect predictor at level 2 represents an implicit “cross–level” interaction with the level 1 predictor, time. While this relation is clearly recognized within the HLM literature, cross–level interactions are not often more closely investigated using classical techniques such as testing of simple slopes and computing regions of significance. Here we demonstrate that methods for testing and probing interactions in the standard regression model can be generalized to a broad class of hierarchical linear models. Within the growth model, these techniques provide essential information for interpreting specifically how the relationships of predictors to the repeated measures change over time. This approach extends naturally to the examination of multiplicative interactions between level 2 variables, which then constitute three–way cross–level interactions with time. We present analytical developments and illustrate the use of these methods using an empirical example drawn from the Longitudinal Study of Optimal Aging.
