Analyzing measurement models of latent variables through multilevel confirmatory factor analysis and hierarchical linear modeling approaches

Confirmatory factor analysis (CFA) is often used in the social sciences to estimate a measurement model in which multiple measurement items are hypothesized to assess a particular latent construct. This article presents the utility of multilevel CFA (MCFA; Muthén, 1991, 1994) and hierarchical linear modeling (HLM; Raudenbush, Rowan, & Kang, 1991) methods in testing measurement models in which the underlying attribute may vary as a function of various levels of observation. An illustrative example using a real dataset is provided in which an unconditional model specification and parameter estimates from the MCFA and HLM are shown. The article demonstrates the comparability of the two methods in estimating measurement parameters of interest (i.e., true variance at levels the measures are used and measurement errors).