Latent variable models for longitudinal data in educational studies

Although there is a variety of statistical methods available for the analysis of longitudinal panel data, two approaches are of particular historical importance: the autoregressive (simplex) model and the latent trajectory (curve) model. However, in educational and social studies the combination of the two approaches can be particularly well-suited in view of analyzing the performance of students over time. Curran and Bollen (2004) have introduced Autoregressive Latent Trajectories (ALT) that integrate a standard LGC with autoregressive relationships between the observed variables. Starting from an application to a real data set, we show how ALT models are particularly useful in deriving a simplified solution in terms of empirical interpretation of the results, in particular in presence of nonlinear pattern of the student achievements over time.