Latent growth modeling allows social behavioral researchers to investigate within-person change and between-person differences in within-person change. Typically, conventional latent growth curve models are applied to continuous variables, where the residuals are assumed to be normally distributed, whereas categorical variables (i.e., binary and ordinal variables), which do not hold to normal distribution assumptions, have been rarely used. This article describes the latent growth curve model with categorical variables, and illustrates applications using Mplus software that are applicable to social behavioral research. The illustrations use marital instability data from the Iowa Youth and Family Project. We close with recommendations for the specification and parameterization of growth models that use both logit and probit link functions.
Keywords: Categorical variables; Latent growth curve model; Latent response variable.