Structural Equation Modeling of Repeated Measures Data: Latent Curve Analysis
Scott L. Hershberger, D.S. Moskowitz · Psychology Press eBooks · 2013
The statistical analysis of repeated measures data over time can be a remarkably challenging task that, if successful, has the potential for allowing significant insight into many important theoretical questions of interest. Over the years, a wide variety of longitudinal statistical models have been proposed to address this challenge, including repeated measures t-tests, analysis of variance ( A N O V A ) , analysis of covariance ( A N C O V A ) , multivariate analysis of variance ( M A N O V A ) , multiple regression, and path analysis. Advances in structural equation modeling (SEM) over the past 25 years have provided many additional statistical methods for analyzing longitudinal data. One S E M method that has had a long and important history within a wide variety of social science research settings is the autoregressive crosslagged ( A R C L ) panel model. However, because of several limitations associated with this modeling approach when applied under certain conditions (e.g., Rogosa, 1995), the past decade has witnessed the rise of an alternative SEM-based analytic approach to modeling longitudinal data, the latent curve model. Although latent curve analysis overcomes a number of limitations associated with the A R C L model, it is not without its own limitations. Applied researchers must be able to weigh the advantages and disadvantages of each of these analytic approaches so that an informed decision can be made about the optimal analytic strategy for evaluating the particular research question at hand (Curran & Bollen, in press). The goal of this chapter is to explicate the advantages and disadvan- tages of using the SEM-based latent curve model in applied longitudinal research. This will be accomplished both through a discussion of the basic concepts and equations underlying latent curve analysis and through an applied example concerning the development of antisocial behavior in children. We begin the chapter with a description of the theoretical framework, specific hypotheses, empirical sample, and measures that will be used in the applied example. We then briefly review the A R C L model and discuss the potential advantages and disadvantages of this analytic strategy for evaluating longitudinal research hypotheses. We follow this with an introduction to latent curve analysis and a detailed application of these models to a set of theoretically derived research questions. Our primary intent is for this chapter to address the needs of applied researchers by providing a detailed pedagogical introduction to the latent curve model that describes the analytic technique and highlights its advantages, limitations, and potential future directions.