Parallel process latent growth curve mediation models (PP-LGCMMs) are frequently used to longitudinally investigate the mediation effects of treatment on the level and change of outcome through the level and change of mediator. An important but often violated assumption in empirical PP-LGCMM analysis is the absence of omitted confounders of the…

Parallel process latent growth curve mediation models (PP-LGCMMs) are frequently used to longitudinally investigate the mediation effects of treatment on the level and change of outcome through the level and change of mediator. An important but often violated assumption in empirical PP-LGCMM analysis is the absence of omitted confounders of the…

Determining the number of factors in exploratory factor analysis (EFA) is crucial because it affects the rest of the analysis and the conclusions of the study. Researchers have developed various methods for deciding the number of factors to retain in EFA, but this remains one of the most difficult decisions in the EFA. The purpose of this study is…

Meta-analytic models for dependent effect sizes have grown increasingly sophisticated over the last few decades, which has created challenges for a priori power calculations. We introduce power approximations for tests of average effect sizes based upon several common approaches for handling dependent effect sizes. In a Monte Carlo simulation, we…

This paper aims to advocate for a balanced approach to model fit evaluation in structural equation modeling (SEM). The ongoing debate surrounding chi-square test statistics and fit indices has been characterized by ambiguity and controversy. Despite the acknowledged limitations of relying solely on the chi-square test, its careful application can…

Latent transition analysis is an informative statistical tool for depicting heterogeneity in learning as latent profiles. We present a Monte Carlo simulation study to guide researchers in selecting fit indices for identifying the correct number of profiles. We simulated data representing profiles of learners within a typical pre- post- follow…

When a response pattern does not fit a selected measurement model, one may resort to robust ability estimation. Two popular robust methods are biweight and Huber weight. So far, research on these methods has been quite limited. This article proposes the maximum a posteriori biweight (BMAP) and Huber weight (HMAP) estimation methods. These methods…

Hybrid autoregressive-latent growth structural equation models for longitudinal data represent a synthesis of the autoregressive and latent growth modeling frameworks. Although these models are conceptually powerful, in practice they may struggle to separate autoregressive and growth-related processes during estimation. This confounding of change…

Despite broad applications of growth curve models, few studies have dealt with a practical issue -- nonnormality of data. Previous studies have used Student's "t" distributions to remedy the nonnormal problems. In this study, robust distributional growth curve models are proposed from a semiparametric Bayesian perspective, in which…

Measurement invariance is crucial for an effective and valid measure of a construct. Invariance holds when the latent trait varies consistently across subgroups; in other words, the mean differences among subgroups are only due to true latent ability differences. Differential item functioning (DIF) occurs when measurement invariance is violated.…

To further understand the properties of data-generation algorithms for multivariate, nonnormal data, two Monte Carlo simulation studies comparing the Vale and Maurelli method and the Headrick fifth-order polynomial method were implemented. Combinations of skewness and kurtosis found in four published articles were run and attention was…

The normal-distribution-based likelihood ratio statistic T[subscript ml] = nF[subscript ml] is widely used for power analysis in structural Equation modeling (SEM). In such an analysis, power and sample size are computed by assuming that T[subscript ml] follows a central chi-square distribution under H[subscript 0] and a noncentral chi-square…

The authors performed a Monte Carlo simulation to empirically investigate the robustness and power of 4 methods in testing mean differences for 2 independent groups under conditions in which 2 populations may not demonstrate the same pattern of nonnormality. The approaches considered were the t test, Wilcoxon rank-sum test, Welch-James test with…

The purpose of this study was to explore the use of robust variance estimation for combining commonly specified multiple regression models and for combining sample-dependent focal slope estimates from diversely specified models. The proposed estimator obviates traditionally required information about the covariance structure of the dependent…

Meta-analysis of time-to-event data has proved difficult in the past because consistent summary statistics often cannot be extracted from published results. The use of individual patient data allows for the re-analysis of each study in a consistent fashion and thus makes meta-analysis of time-to-event data feasible. Time-to-event data can be…