Longitudinal data analysis with structural equations

In this paper we review different structural equation models for the analysis of longitudinal data: (a) univariate models of observable variables, (b) multivariate models of observable variables, (c) models with latent variables, (d) models that are unconditioned or conditioned to other variables (depending on the variability of the independent variables: time-varying or time-invariant, and depending on the type of independent variables: of latent variables or of observable variables), (e) models with interaction of variables, (f) models with non-linear variables, (g) models with a constant, (h) with single level and multilevel measurement, and (i) other advances in SEM of longitudinal data (latent growth curve model, latent difference score, etc.). We have paid more attention to the interaction of variables and to non-linear transformations of variables because they are not frequently used in empirical investigation. They do, however, offer interesting possibilities to researchers who wish to verify relations between the variables they obtain. Potential applications are described, with their advantages and disadvantages