Semiparametric Bayesian Methods in Growth Curve Modeling for Nonnormal Data Analysis

Semiparametric Bayesian methods have been proposed in the literature for growth curve modeling to reduce the adverse effect of having nonnormal data. The normality assumption of measurement errors in traditional growth curve models was {replaced} by a random distribution with Dirichlet process mixture priors. However, both the random effects and measurement errors are equally likely to be nonnormal. Therefore, in this study, three types of robust distributional growth curve models are proposed from a semiparametric Bayesian perspective, in which random coefficients or measurement errors follow either normal distributions or unknown random distributions with Dirichlet process mixture priors. Based on a Monte Carlo simulation study, we evaluate the performance of the robust models and demonstrate that selecting an appropriate model for practical data analyses is very important, by comparing the three types of robust distributional models as well as the traditional growth curve models with the normality assumption. We also provide a straightforward strategy to select the appropriate model.

Computational options for standard errors and test statistics with incomplete normal and nonnormal data in SEM

This article provides an overview of different computational options for inference following normal theory maximum likelihood (ML) estimation in structural equation modeling (SEM) with incomplete normal and nonnormal data. Complete data are covered as a special case. These computational options include whether the information matrix is observed or expected, whether the observed information matrix is estimated numerically or using an analytic asymptotic approximation, and whether the information matrix and the outer product matrix of the score vector are evaluated at the saturated or at the structured estimates. A variety of different standard errors and robust test statistics become possible by varying these options. We review the asymptotic properties of these computational variations, and we show how to obtain them using lavaan in R. We hope that this article will encourage methodologists to study the impact of the available computational options on the performance of standard errors and test statistics in SEM.

Mitigating Selection Bias: A Bayesian Approach to Two-stage Causal Modeling With Instrumental Variables for Nonnormal Missing Data

This study proposes a two-stage causal modeling with instrumental variables to mitigate selection bias, provide correct standard error estimates, and address nonnormal and missing data issues simultaneously. Bayesian methods are used for model estimation. Robust methods with Student’s t distributions are used to account for nonnormal data. Ignorable missing data are handled by multiple imputation techniques, while nonignorable missing data are handled by an added-on selection model structure. In addition to categorical treatment data, this study extends the work to continuous treatment variables. Monte Carlo simulation studies are conducted showing that the proposed Bayesian approach can well address common issues in existing methods. We provide a real data example on the early childhood relative age effect study to illustrate the application of the proposed method. The proposed method can be easily implemented using the R software package "ALMOND" (Analysis of Local Average Treatment Effect for missing or/and Nonnormal Data).