Evaluating latent variable growth models through ex post simulation

This article considers the use elf ex post (historical) simulation statisti cs as a means of evaluating latent variable growth models. Ex post simulati on involves using the estimated parameters of a latent variable growth mode l to track the known historical values of an outcome of interest. Such meth ods of evaluating temporal models rr ere developed primarily in applied eco nomic forecasting and have been known for some time. This paper applies a v ariety of simulation quality statistics to latent variable growth models. I n particular Theil's (1966) inequality coefficient, bias proportion, varian ce proportion, and covariance proportion are used to gauge the simulation a dequacy of growth models. An cli,application to the study of change in scie nce achievement using data from the Longitudinal Study of American Youth is provided to illustrate the methodology. The results illustrate the importa nce of using these measures us adjuncts to more traditional forms of model evaluation, especially if one is considering the use of these models for su bsequent forecasting or other policy purposes.