Typical for developmental psychology are models that capture change over time, such as latent growth (mixture) models and to a lesser extent cross-lagged panel models too. Such models have typically been applied aiming to capture change over time in individuals.
In a latent growth model, the time or measurement occasion variable is defined in the measurement model of the latent factors. To be more specific consecutive measurements are modeled by a latent variable for the intercept of the growth curve, and a second latent variable for the slope of the curve . With latent growth analysis, I refer to person-centred techniques to estimate individuals developing over time. Latent growth modelling assumes that all individuals are drawn from one population. To be more specific, consecutive measurements are summarized by a growth trajectory modeled by latent variables, typically denoting the intercept of the growth curve, the linear slope of the curve and the deviation of linearity.
The development over time can be combined with a mixture component to estimate trajectory membership. Mixture modelling means that growth parameters (i.e., intercept, slope, etc.) vary across a number of pre-specified, unobserved subpopulations. These subpopulations are established through scores on one or more categorical latent variables. These additional variables allow for calculating growth trajectories per group. Hence, the usage of such variables results in separate latent growth models for each (unobserved) group, each with its unique set of growth parameters.
In this project I have published on applying longitudinal models to empirical data and how to properly report on LGMM models. Furthermore, I study the Bayesian counterpart of longitudinal models, and then particularly how the prior information can best be defined for small samples . Several of such papers are currently under review. Once these have been accepted, more information on them will be made available.