Among all, Cronbach's Alpha and McDonald's Omega are commonly used for reliability estimations. The alpha uses inter-item correlations while omega is based on a factor analysis result. This study uses simulated ordinal data sets to test whether the alpha and omega produce different estimates. Their performances were compared according to the…

There is a great deal of research about item response theory (IRT) conducted by simulations. Item and ability parameters are estimated with varying numbers of replications under different test conditions. However, it is not clear what the appropriate number of replications should be. The aim of the current study is to develop guidelines for the…

Analysts of discrete data often face the challenge of managing the tendency of inflation on certain values. When treated improperly, such phenomenon may lead to biased estimates and incorrect inferences. This study extends the existing literature on single-value inflated models and develops a general framework to handle variables with more than…

Previous research includes frequent admonitions regarding the importance of establishing connectivity in data collection designs prior to the application of Rasch models. However, details regarding the influence of characteristics of the linking sets used to establish connections among facets, such as locations on the latent variable, model-data…

This study proposes a two-part model that includes components for reading accuracy and reading speed. The speed component is a log-normal factor model, for which speed data are measured by reading time for each sentence being assessed. The accuracy component is a binomial-count factor model, where the accuracy data are measured by the number of…

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…

Using Monte Carlo simulations, this research examined the performance of four missing data methods in SEM under different multivariate distributional conditions. The effects of four independent variables (sample size, missing proportion, distribution shape, and factor loading magnitude) were investigated on six outcome variables: convergence rate,…

Latent variables are common in psychological research. Research questions involving the interaction of two variables are likewise quite common. Methods for estimating and interpreting interactions between latent variables within a structural equation modeling framework have recently become available. The latent moderated structural equations (LMS)…

Given that the root mean square error of approximation (RMSEA) is currently one of the most popular measures of goodness-of-model fit within structural equation modeling (SEM), it is important to know how well the RMSEA performs in models with small degrees of freedom ("df"). Unfortunately, most previous work on the RMSEA and its…

Item response theory (IRT) has gained an increasing popularity in large-scale educational and psychological testing situations because of its theoretical advantages over classical test theory. Unidimensional graded response models (GRMs) are useful when polytomous response items are designed to measure a unified latent trait. They are limited in…

The item response times (RTs) collected from computerized testing represent an underutilized type of information about items and examinees. In addition to knowing the examinees' responses to each item, we can investigate the amount of time examinees spend on each item. Current models for RTs mainly focus on parametric models, which have the…

Muthen and Asparouhov (2012) have proposed and demonstrated an approach to model specification and estimation in structural equation modeling (SEM) using Bayesian methods. Their contribution builds on previous work in this area by (a) focusing on the translation of conventional SEM models into a Bayesian framework wherein parameters fixed at zero…

The usefulness of the l[subscript z] person-fit index was investigated with achievement test data from 20 exams given to more than 3,200 college students. Results for three methods of estimating ? showed that the distributions of l[subscript z] were not consistent with its theoretical distribution, resulting in general overfit to the item response…

In Ramsay curve item response theory (RC-IRT, Woods & Thissen, 2006) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's (1981) EM algorithm, which yields maximum marginal likelihood estimates. This method, however,…

Interest in testing interaction terms within the latent variable modeling framework has been on the rise in recent years. However, little is known about the influence of nonnormality and model misspecification on such models that involve latent variable interactions. The authors used Mattson's data generation method to control for latent variable…