Using a Multivariate Multilevel Polytomous Item Response Theory Model to Study Parallel Processes of Change: The Dynamic Association Between Adolescents' Social Isolation and Engagement With Delinquent Peers in the National Youth Survey.

The application of multidimensional item response theory models to repeated observations has demonstrated great promise in developmental research. It allows researchers to take into consideration both the characteristics of item response and measurement error in longitudinal trajectory analysis, which improves the reliability and validity of the latent growth curve (LGC) model. The purpose of this study is to demonstrate the potential of Bayesian methods and the utility of a comprehensive modeling framework, the one combining a measurement model (e.g., a multidimensional graded response model, MGRM) with a structural model (e.g., an associative latent growth curve analysis, ALGC). All analyses are implemented in WinBUGS 1.4.3 ( Spiegelhalter, Thomas, Best, & Lunn, 2003 ), which allows researchers to use Markov chain Monte Carlo simulation methods to fit complex statistical models and circumvent intractable analytic or numerical integrations. The utility of this MGRM-ALGC modeling framework was investigated with both simulated and empirical data, and promising results were obtained. As the results indicate, being a flexible multivariate multilevel model, this MGRM-ALGC model not only produces item parameter estimates that are readily estimable and interpretable but also estimates the corresponding covariation in the developmental dimensions. In terms of substantive interpretation, as adolescents perceived themselves more socially isolated, the chance that they are engaged with delinquent peers becomes profoundly larger. Generally, boys have a higher initial exposure extent than girls. However, there is no gender difference associated with other latent growth parameters.