Latent Growth Models represent repeated measures of dependent variables as a function of time and other measures. Such longitudinal data share the features that the same subjects are observed repeatedly over time, and on the same tests (or parallel versions), and at known times. In latent growth modeling, the relative standing of an individual at each time is modeled as a function of an underlying growth process, with the best parameter values for that growth process being fitted to each individual. These models have grown in use in social and behavioral research since it was shown that they can be fitted as a restricted common factor model in the
structural equation modeling framework. for a comprehensive review) Although many applications of latent growth curve models estimate only initial level and slope components, more complex models can be estimated. Models with higher order components, e.g., quadratic, cubic, do not predict even-increasing variance, but require more than two occasions of measurement. It is also possible to fit models based on growth curves with functional forms, often versions of the
generalised logistic growth such as the
logistic,
exponential or
Gompertz functions. Though straightforward to fit with versatile software such as
OpenMx, these more complex models cannot be fitted with SEM packages in which path coefficients are restricted to being simple constants or free parameters, and cannot be functions of free parameters and data. Discontinuous models where the growth pattern changes around a time point (for example, is different before and after an event) can also be fit in SEM software. Similar questions can also be answered using a
multilevel model approach. == References ==