A latent growth curve model from the perspective of a structural equation model

Abstract

Latent growth curve modeling (LGCM) is a multivariate technique suited for explaining change over time. In this dissertation, the theoretical background needed to address the specification and estimation of a latent growth curve model from the perspective of a structural equation model (SEM), is provided. SEM is a collection of statistical methods used to examine the relationship between one or more independent variables and between one or more dependent variables. These variables may be both observed and unobserved (latent). In LGCM, the observed data is the repeated measures data obtained on the variables of interest and the latent variables that represent aspects of change in the variables of interest. This theoretical background is then used to fit a latent growth curve model to a longitudinal data provided by a local gaming company. The main variable of interest in this dataset is customer deposits monitored over a 12-month period. The relationship between customers’ characteristics and changes in the amount deposited over time are also investigated. A simulation study is then also carried out to investigate the relative performance of the maximum likelihood (ML) estimator in estimating parameters of a latent growth curve model under multivariate normality of the repeated measures data and deviations from multivariate normality, and under varying sample sizes.