Latent Variable Modeling of Multilevel Intrinsic Motivation Data

Data in social science research often have a multilevel structure, with observations on individuals nested within groups. However, such data have been routinely analyzed at the individual level, whereas the group level variation has been ignored. Recent developments in multilevel covariance structure modeling (MCSM; Muthén, 1994) provide a useful statistical tool for analyzing sources of variation due to both within- and between-group influences. The purpose of this study is to illustrate the use of multilevel confirmatory factor analysis (MCFA) via a didactic example of a 2-level (student vs. class) analysis of exercise intrinsic motivation to experience sensations (IM-ES) data. Application of MCFA revealed substantial variation in the IM-ES at both student and class levels. In addition, predictors designed to explain the between-class levels of IM-ES (class size, type of instructor, and type of activity) significantly predicted the class-level variation in the IM-ES. The study demonstrated the merit of using multilevel analytic techniques in substantive research where data have multilevel components.