Examining Residual Correlations in Latent Transition Analysis: A Simulation Study

• In Event: Methodological Advances in Longitudinal Mixture Modeling

Abstract

Latent transition analysis (LTA) has become increasingly utilized in social science research in recent years. When repeated measures are administered in longitudinal contexts, it is possible for repeated observed items to exhibit residual correlations that are unexplained by the latent variables. This may be due to a number of reasons such as changes in the individuals’ perceptions of the items over time or changes in skill levels unrelated to the latent variable being measured. Asparouhov and Muthén (2015) conducted a simulation study (using both latent class analysis and LTA) demonstrating that when these residual correlations are ignored, latent class proportions can be biased as the model will attempt to correct for these missing correlations among observed indicators in the latent class variables. However, their study was focused on the absence or presence of residual correlations and missing data. Additionally, to date there have been no further simulation studies or research on residual correlations among indicators across time in an LTA context. This simulation study builds upon the work of Asparouhov and Muthén (2015) by varying other conditions and parameters not examined in their paper.
All simulations were conducted in Mplus 8.3 (Muthén & Muthén, 1998-2017). Data for an LTA (with sample sizes of 200, 500, and 1000) were generated with ordered three-class models at each of two timepoints. In addition to varying sample size, this study also varied the number of indicators (four and eight) and the number of residual correlations (none, half, all) across time that were included in the models. The residual correlations were specified to be uniform across latent classes and were set at a moderate value of 0.4. Preliminary results suggest that ignoring residual correlations produces severely biased class proportion and transition probability estimates in smaller samples and with fewer indicators. At larger sample sizes, omitting half or all of the residual correlations produced biased transition probabilities, but class proportions were not severely affected. Additionally, coverage remained high when estimating class proportions, but was low for transition probabilities. Further analyses will also examine effects when the magnitudes of the residual correlations are varied.
In addition to the simulation study, this paper provides an applied LTA example using reading achievement data collected from N = 459 students in fall and spring of first grade. The observed indicators were six dichotomized repeated measures assessing phonological awareness, word reading, and linguistic comprehension. This demonstration is presented in two parts. First, after identifying a preferred LTA model without residual correlations, two approaches for examining potential residual correlations that may be included are demonstrated: 1) bivariate Pearson testing, and 2) all uniform associations. Second, the results from including residual correlations from each approach are presented and compared. Mplus syntax will be provided.

References:
Asparouhov, T. & Muthén, B. (2015). Residual associations in latent class and latent transition analysis. Structural Equation Modeling: A Multidisciplinary Journal, 22, 169-177.

Muthén, L.K. & Muthén, B.O. (1998-2017). Mplus User’s Guide. Eighth Edition. Los Angeles,
CA: Muthén & Muthén.

Authors

• Ryan Grimm, SRI International

• Karen L. Nylund-Gibson, University of California - Santa Barbara