Evaluating Latent Variable Growth Models Through Ex Post Simulation

This article considers the use of ex post (historical) simulation statistics as a means of evaluating latent variable growth models. Ex post simulation involves using the estimated parameters of a latent variable growth model to track the known historical values of an outcome of interest. Such methods of evaluating temporal models were developed primarily in applied economic forecasting and have been known for some time. This paper applies a variety of simulation quality statistics to latent variable growth models. In particular, Theil’s (1966) inequality coefficient, bias proportion, variance proportion, and covariance proportion are used to gauge the simulation adequacy of growth models. An application to the study of change in science achievement using data from the Longitudinal Study of American Youth is provided to illustrate the methodology. The results illustrate the importance of using these measures as adjuncts to more traditional forms of model evaluation, especially if one is considering the use of these models for subsequent forecasting or other policy purposes.