Recent Changes Leading to Subsequent Changes: Extensions of Multivariate Latent Difference Score Models

Latent difference score models (e.g., McArdle & Hamagami, 2001 McArdle, J. J. 2001. “A latent difference score approach to longitudinal dynamic structural analysis.”. In Structural equation modeling: Present and future Edited by: Cudeck, R., du Toit, S. and Sorbom, D. 342–380. Lincolnwood, IL: Scientific Software International..  [Google Scholar]) are extended to include effects from prior changes to subsequent changes. This extension of latent difference scores allows for testing hypotheses where recent changes, as opposed to recent levels, are a primary predictor of subsequent changes. These models are applied to bivariate longitudinal data collected as part of the Baltimore Longitudinal Study of Aging on memory performance, measured by the California Verbal Learning Test, and lateral ventricle size, measured by structural MRIs. Results indicate that recent increases in the lateral ventricle size were a leading indicator of subsequent declines in memory performance from age 60 to 90.     

An Evaluation of Latent Growth Models for Propensity Score Matched Groups

Because random assignment is not possible in observational studies, estimates of treatment effects might be biased due to selection on observable and unobservable variables. To strengthen causal inference in longitudinal observational studies of multiple treatments, we present 4 latent growth models for propensity score matched groups, and evaluate their performance with a Monte Carlo simulation study. We found that the 4 models performed similarly with respect to model fit, bias of parameter estimates, Type I error, and power to test the treatment effect. To demonstrate a multigroup latent growth model with dummy treatment indicators, we estimated the effect of students changing schools during elementary school years on their reading and mathematics achievement, using data from the Early Childhood Longitudinal Study Kindergarten Cohort.     

Monte Carlo Confidence Intervals for Complex Functions of Indirect Effects

One challenge in mediation analysis is to generate a confidence interval (CI) with high coverage and power that maintains a nominal significance level for any well-defined function of indirect and direct effects in the general context of structural equation modeling (SEM). This study discusses a proposed Monte Carlo extension that finds the CIs for any well-defined function of the coefficients of SEM such as the product of k coefficients and the ratio of the contrasts of indirect effects, using the Monte Carlo method. Finally, we conduct a small-scale simulation study to compare CIs produced by the Monte Carlo, nonparametric bootstrap, and asymptotic-delta methods. Based on our simulation study, we recommend researchers use the Monte Carlo method to test a complex function of indirect effects.     

Mediated Effects with the Parallel Process Latent Growth Model: An Evaluation of Methods for Testing Mediation in the Presence of Nonnormal Data

This Monte Carlo simulation study investigated the impact of nonnormality on estimating and testing mediated effects with the parallel process latent growth model and 3 popular methods for testing the mediated effect (i.e., Sobel’s test, the asymmetric confidence limits, and the bias-corrected bootstrap). It was found that nonnormality had little effect on the estimates of the mediated effect, standard errors, empirical Type I error, and power rates in most conditions. In terms of empirical Type I error and power rates, the bias-corrected bootstrap performed best. Sobel’s test produced very conservative Type I error rates when the estimated mediated effect and standard error had a relationship, but when the relationship was weak or did not exist, the Type I error was closer to the nominal .05 value.     

On the Performance of Likelihood-Based Difference Tests in Nonlinear Structural Equation Models

This article investigates likelihood-based difference statistics for testing nonlinear effects in structural equation modeling using the latent moderated structural equations (LMS) approach. In addition to the standard difference statistic T_D, 2 robust statistics have been developed in the literature to ensure valid results under the conditions of nonnormality or small sample sizes: the robust T_DR and the “strictly positive” T_DRP. These robust statistics have not been examined in combination with LMS yet. In 2 Monte Carlo studies we investigate the performance of these methods for testing quadratic or interaction effects subject to different sources of nonnormality, nonnormality due to the nonlinear terms, and nonnormality due to the distribution of the predictor variables. The results indicate that T_D is preferable to both T_DR and T_DRP. Under the condition of strong nonlinear effects and nonnormal predictors, T_DR often produced negative differences and T_DRP showed no desirable power.     

Accuracy of Estimates and Statistical Power for Testing Meditation in Latent Growth Curve Modeling

The latent growth curve modeling (LGCM) approach has been increasingly utilized to investigate longitudinal mediation. However, little is known about the accuracy of the estimates and statistical power when mediation is evaluated in the LGCM framework. A simulation study was conducted to address these issues under various conditions including sample size, effect size of mediated effect, number of measurement occasions, and R ₂ of measured variables. In general, the results showed that relatively large samples were needed to accurately estimate the mediated effects and to have adequate statistical power, when testing mediation in the LGCM framework. Guidelines for designing studies to examine longitudinal mediation and ways to improve the accuracy of the estimates and statistical power were discussed.     

Statistical Power of the Multiple Domain Latent Growth Model for Detecting Group Differences

The latent growth model (LGM) in structural equation modeling (SEM) may be extended to allow for the modeling of associations among multiple latent growth trajectories, resulting in a multiple domain latent growth model (MDLGM). While the MDLGM is conceived as a more powerful multivariate analysis technique, the examination of its methodological performance is very limited. Hence, the present study compared the power of the MDLGM with that of a set of univariate LGMs for detecting group differences in growth rates over time using a Monte Carlo study with a two-group and two-domain design. The results indicated that there were different scenarios where the power rates for the MDLGM were greater than that of the set of LGMs (and vice versa) due to a joint function of the two domains’ intercorrelation size and the group difference effect size.     

Estimating Latent Variable Interactions with the Unconstrained Approach: A Comparison of Methods to Form Product Indicators for Large,Unequal Numbers of Items

This Monte Carlo simulation study investigated methods of forming product indicators for the unconstrained approach for latent variable interaction estimation when the exogenous factors are measured by large and unequal numbers of indicators. Product indicators were created based on multiplying parcels of the larger scale by indicators of the smaller scale, multiplying the three most reliable indicators of each scale matched by reliability, and matching items by reliability to create as many product indicators as the number of indicators of the smallest scale. The unconstrained approach was compared with the latent moderated structural equations (LMS) approach. All methods considered provided unbiased parameter estimates. Unbiased standard errors were obtained in all conditions with the LMS approach and when the sample size was large with the unconstrained approach. Power levels to test the latent interaction and Type I error rates were similar for all methods but slightly better for the LMS approach.