ABSTRACT
In studies of psychological change, researchers seek statistical models that are developmentally meaningful and provide a reasonable fit to the data. They also seek inferences that are fairly insensitive to questionable assumptions about the random behavior of their data. This chapter compares, contrasts, and integrates two modeling approaches in light of these concerns: a hierarchical linear model and a multivariate model for incomplete data. If the complete data are multivariate normal with homogeneous co-variance structure, now-standard hierarchical models are submodels of the multivariate model. This principal can be exploited to compare the fit of alternative hierarchical models with each other and with an unrestricted multivariate model. However, hierarchical models often imply heterogeneity of covariance structure and are therefore more general than the conventional multivariate models for incomplete data. Both models can readily be extended to include the clustering within groups of repeatedly observed participants. Robust standard errors for the fixed regression coefficients are available within both approaches. Taken together, these approaches allow a thorough investigation of the sensitivity of key inferences to alternative model assumptions. The two approaches are illustrated by reanalysis of data from two large-scale longitudinal studies.
