Dominance analysis (DA) is a very useful tool for ordering independent variables in a regression model based on their relative importance in explaining variance in the dependent variable. This approach, which was originally described by Budescu, has recently been extended to use with structural equation models examining relationships among latent…

Prior studies investigating the effects of non-normality in structural equation modeling typically induced non-normality in the indicator variables. This procedure neglects the factor analytic structure of the data, which is defined as the sum of latent variables and errors, so it is unclear whether previous results hold if the source of…

One important issue in Bayesian estimation is the determination of an effective informative prior. In hierarchical Bayes models, the uncertainty of hyperparameters in a prior can be further modeled via their own priors, namely, hyper priors. This study introduces a framework to construct hyper priors for both the mean and the variance…

We examined the effect of estimation methods, maximum likelihood (ML), unweighted least squares (ULS), and diagonally weighted least squares (DWLS), on three population SEM (structural equation modeling) fit indices: the root mean square error of approximation (RMSEA), the comparative fit index (CFI), and the standardized root mean square residual…

This study discusses quantile regression methodology and its usefulness in education and social science research. First, quantile regression is defined and its advantages vis-à-vis vis ordinary least squares regression are illustrated. Second, specific comparisons are made between ordinary least squares and quantile regression methods. Third, the…

A simulation study was conducted to investigate the model size effect when confirmatory factor analysis (CFA) models include many ordinal items. CFA models including between 15 and 120 ordinal items were analyzed with mean- and variance-adjusted weighted least squares to determine how varying sample size, number of ordered categories, and…

When item scores are ordered categorical, categorical omega can be computed based on the parameter estimates from a factor analysis model using frequentist estimators such as diagonally weighted least squares. When the sample size is relatively small and thresholds are different across items, using diagonally weighted least squares can yield a…

Evaluations of measurement invariance provide essential construct validity evidence--a prerequisite for seeking meaning in psychological and educational research and ensuring fair testing procedures in high-stakes settings. However, the quality of such evidence is partly dependent on the validity of the resulting statistical conclusions. Type I or…

Cluster randomized trials involving participants nested within intact treatment and control groups are commonly performed in various educational, psychological, and biomedical studies. However, recruiting and retaining intact groups present various practical, financial, and logistical challenges to evaluators and often, cluster randomized trials…