Bayesian estimations of complex regression models with high-dimensional parameter spaces require advanced priors, capable of addressing both sparsity and multicollinearity in the data. The Dirichlet-horseshoe, a new prior distribution that combines and expands on the concepts of the regularized horseshoe and the Dirichlet-Laplace priors, is a…

The Bayesian piecewise growth model (PGM) is a useful class of models for analyzing nonlinear change processes that consist of distinct growth phases. In applications of Bayesian PGMs, it is important to accurately capture growth trajectories and carefully consider knot placements. The presence of missing data is another challenge researchers…

This study aims to estimate the latent interaction effect in the CLPM model through a two-step multiple imputation analysis. The estimation of within x within and between x within latent interaction under the CLPM model framework is compared between the one-step Bayesian LMS method and the two-step multiple imputation analysis through a simulation…

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…

Within the frequentist structural equation modeling (SEM) framework, adjudicating model quality through measures of fit has been an active area of methodological research. Complicating this conversation is research revealing that a higher quality measurement portion of a SEM can result in poorer estimates of overall model fit than lower quality…

We present a method for Bayesian structural equation modeling of sample correlation matrices as correlation structures. The method transforms the sample correlation matrix to an unbounded vector using the matrix logarithm function. Bayesian inference about the unbounded vector is performed assuming a multivariate-normal likelihood, with a mean…

Latent class analysis (LCA) is a widely used technique for detecting unobserved population heterogeneity in cross-sectional data. Despite its popularity, the performance of LCA is not well understood. In this study, we evaluate the performance of LCA with binary data by examining classification accuracy, parameter estimation accuracy, and coverage…

Model-Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) is a limited information, equation-by-equation, noniterative estimator for latent variable models. Associated with this estimator are equation-specific tests of model misspecification. One issue with equation-specific tests is that they lack specificity, in that they indicate…

Real data are unlikely to be exactly normally distributed. Ignoring non-normality will cause misleading and unreliable parameter estimates, standard error estimates, and model fit statistics. For non-normal data, researchers have proposed a distributionally-weighted least squares (DLS) estimator to combines the normal theory based generalized…

We extended current knowledge by examining the performance of several Bayesian model fit and comparison indices through a simulation study using the confirmatory factor analysis. Our goal was to determine whether commonly implemented Bayesian indices can detect specification errors. Specifically, we wanted to uncover any differences in detecting…

Dynamic structural equation modeling (DSEM) is a useful technique for analyzing intensive longitudinal data. A challenge of applying DSEM is the missing data problem. The impact of missing data on DSEM, especially on widely applied DSEM such as the two-level vector autoregressive (VAR) cross-lagged models, however, is understudied. To fill the…

In parallel process latent growth curve mediation models, the mediation pathways from treatment to the intercept or slope of outcome through the intercept or slope of mediator are often of interest. In this study, we developed causal mediation analysis methods for these mediation pathways. Particularly, we provided causal definitions and…

Mediation analysis is widely applied in various fields of science, such as psychology, epidemiology, and sociology. In practice, many psychological and behavioral phenomena are dynamic, and the corresponding mediation effects are expected to change over time. However, most existing mediation methods assume a static mediation effect over time,…

This study examined the false positive (FP) rates and sensitivity of Bayesian fit indices to structural misspecification in Bayesian structural equation modeling. The impact of measurement quality, sample size, model size, the magnitude of misspecified path effect, and the choice or prior on the performance of the fit indices was also…

The present work focuses on the performance of two types of shrinkage priors--the horseshoe prior and the recently developed regularized horseshoe prior--in the context of inducing sparsity in path analysis and growth curve models. Prior research has shown that these horseshoe priors induce sparsity by at least as much as the "gold…