The Misspecification of the Covariance Structures in Multilevel Models for Single-Case Data: A Monte Carlo Simulation Study

The impact of misspecifying covariance matrices at the second and third levels of the three-level model is evaluated. Results indicate that ignoring existing covariance has no effect on the treatment effect estimate. In addition, the between-case variance estimates are unbiased when covariance is either modeled or ignored. If the research interest lies in the between-study variance estimate, including at least 30 studies is warranted. Modeling covariance does not result in less biased between-study variance estimates as the between-study covariance estimate is biased. When the research interest lies in the between-case covariance, the model including covariance results in unbiased between-case variance estimates. The three-level model appears to be less appropriate for estimating between-study variance if fewer than 30 studies are included.     

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.     

Growth Mixture Modeling With Nonnormal Distributions: Implications for Data Transformation

This study investigated the extent to which class-specific parameter estimates are biased by the within-class normality assumption in nonnormal growth mixture modeling (GMM). Monte Carlo simulations for nonnormal GMM were conducted to analyze and compare two strategies for obtaining unbiased parameter estimates: relaxing the within-class normality assumption and using data transformation on repeated measures. Based on unconditional GMM with two latent trajectories, data were generated under different sample sizes (300, 800, and 1500), skewness (0.7, 1.2, and 1.6) and kurtosis (2 and 4) of outcomes, numbers of time points (4 and 8), and class proportions (0.5:0.5 and 0.25:0.75). Of the four distributions, it was found that skew-t GMM had the highest accuracy in terms of parameter estimation. In GMM based on data transformations, the adjusted logarithmic method was more effective in obtaining unbiased parameter estimates than the use of van der Waerden quantile normal scores. Even though adjusted logarithmic transformation in nonnormal GMM reduced computation time, skew-t GMM produced much more accurate estimation and was more robust over a range of simulation conditions. This study is significant in that it considers different levels of kurtosis and class proportions, which has not been investigated in depth in previous studies. The present study is also meaningful in that investigated the applicability of data transformation to nonnormal GMM.     

Alternatives to Multilevel Modeling for the Analysis of Clustered Data

Multilevel modeling has grown in use over the years as a way to deal with the nonindependent nature of observations found in clustered data. However, other alternatives to multilevel modeling are available that can account for observations nested within clusters, including the use of Taylor series linearization for variance estimation, the design effect adjusted standard errors approach, and fixed effects modeling. Using 1,000 replications of 12 conditions with varied Level 1 and Level 2 sample sizes, the author compared parameter estimates, standard errors, and statistical significance using various alternative procedures. Results indicate that several acceptable procedures can be used in lieu of or together with multilevel modeling, depending on the type of research question asked and the number of clusters under investigation. Guidelines for applied researchers are discussed.     

The Actor–Partner Interdependence Model for Longitudinal Dyadic Data: An Implementation in the SEM Framework

In dyadic research, the actor–partner interdependence model (APIM) is widely used to model the effect of a predictor measured across dyad members on one’s own and one’s partner outcome. When such dyadic data are measured repeatedly over time, both the non-independence within couples and the non-independence over time need to be accounted for. In this paper, we present a longitudinal extension of the APIM, the L-APIM, that allows for both stable and time-varying sources of non-independence. Its implementation is readily available in multilevel software, such as proc mixed in SAS, but is lacking in the structural equation modeling (SEM) framework. We tackle the computational challenges associated with its SEM-implementation and propose a user-friendly free application for the L-APIM, which can be found at http://fgisteli.shinyapps.io/Shiny_LDD. As an illustration, we explore the actor and partner effects of positive relationship feelings on next day’s intimacy using 3-week diary data of 66 heterosexual couples.     

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.