In Savalei's (2011) simulation that evaluated the performance of polychoric correlation estimates in small samples, two methods for treating zero-frequency cells, adding 0.5 (ADD) and doing nothing (NONE), were compared. Savalei tentatively suggested using ADD for binary data and NONE for data with three or more categories. Yet, Savalei's…

Estimating confidence intervals (CIs) for the correlation has been a challenge because the correlation sampling distribution changes depending on the correlation magnitude. The Fisher z-transformation was one of the first attempts at estimating correlation CIs but has historically shown to not have acceptable coverage probability if data were…

We consider Bayesian estimation of a hierarchical linear model (HLM) from partially observed data, assumed to be missing at random, and small sample sizes. A vector of continuous covariates C includes cluster-level partially observed covariates with interaction effects. Due to small sample sizes from 37 patient-physician encounters repeatedly…

Numerous methods exist to determine the optimal number of classes when using latent profile analysis (LPA), but none are consistently correct. Recently, the likelihood incremental percentage per parameter (LI3P) was proposed as a model effect-size measure. To evaluate the LI3P more thoroughly, we simulated 50,000 datasets, manipulating factors…

Marginal maximum likelihood, a common estimation method for item response theory models, is not inherently a Bayesian procedure. However, due to estimation difficulties, Bayesian priors are often applied to the likelihood when estimating 3PL models, especially with small samples. Little focus has been placed on choosing the priors for marginal…

In statistics classes, the central limit theorem has been demonstrated using simulation-based illustrations. Known population distributions such as a uniform or exponential distribution are often used to consider the behavior of the sample mean in simulated samples. Unlike such simulations, a number of real-data-based simulations are here…

The purpose of this study was to compare calibration and linking methods for placing pretest item parameter estimates on the item pool scale in a 1-3 computerized multistage adaptive testing design in terms of item parameter recovery. Two models were used: embedded-section, in which pretest items were administered within a separate module, and…

To reduce the chance of Heywood cases or nonconvergence in estimating the 2PL or the 3PL model in the marginal maximum likelihood with the expectation-maximization (MML-EM) estimation method, priors for the item slope parameter in the 2PL model or for the pseudo-guessing parameter in the 3PL model can be used and the marginal maximum a posteriori…

We examine the accuracy of p values obtained using the asymptotic mean and variance (MV) correction to the distribution of the sample standardized root mean squared residual (SRMR) proposed by Maydeu-Olivares to assess the exact fit of SEM models. In a simulation study, we found that under normality, the MV-corrected SRMR statistic provides…

We examined the performance of coefficient alpha and its potential competitors (ordinal alpha, omega total, Revelle's omega total [omega RT], omega hierarchical [omega h], greatest lower bound [GLB], and coefficient "H") with continuous and discrete data having different types of non-normality. Results showed the estimation bias was…

In social and behavioral sciences, data are typically not normally distributed, which can invalidate hypothesis testing and lead to unreliable results when being analyzed by methods developed for normal data. The existing methods of generating multivariate non-normal data typically create data according to specific univariate marginal measures…

Two recent publications in "Educational and Psychological Measurement" advocated that researchers consider using the a priori procedure. According to this procedure, the researcher specifies, prior to data collection, how close she wishes her sample mean(s) to be to the corresponding population mean(s), and the desired probability of…

This article describes an extension to the use of heteroskedastic ordered probit (HETOP) models to estimate latent distributional parameters from grouped, ordered-categorical data by pooling across multiple waves of data. We illustrate the method with aggregate proficiency data reporting the number of students in schools or districts scoring in…

In social and behavioral sciences, data are typically not normally distributed, which can invalidate hypothesis testing and lead to unreliable results when being analyzed by methods developed for normal data. The existing methods of generating multivariate non-normal data typically create data according to specific univariate marginal measures…

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…