Over the last four decades, meta-analysis has proven to be a vital analysis strategy in educational research for synthesizing research findings from different studies. When synthesizing studies in a meta-analysis, it is common to assume that the true underlying effect varies from study to study, as studies will differ in design, participants,…

Factor mixture modeling (FMM) is generally complex with both unobserved categorical and unobserved continuous variables. We explore the potential of item parceling to reduce the model complexity of FMM and improve convergence and class enumeration accordingly. To this end, we conduct Monte Carlo simulations with three types of data, continuous,…

The four-parameter logistic (4PL) Item Response Theory (IRT) model has recently been reconsidered in the literature due to the advances in the statistical modeling software and the recent developments in the estimation of the 4PL IRT model parameters. The current simulation study evaluated the performance of expectation-maximization (EM),…

A Monte Carlo simulation study was conducted to compare fit indices used for detecting the correct latent class in three dichotomous mixture item response theory (IRT) models. Ten indices were considered: Akaike's information criterion (AIC), the corrected AIC (AICc), Bayesian information criterion (BIC), consistent AIC (CAIC), Draper's…

We propose a new item response theory growth model with item-specific learning parameters, or ISLP, and two variations of this model. In the ISLP model, either items or blocks of items have their own learning parameters. This model may be used to improve the efficiency of learning in a formative assessment. We show ways that the ISLP model's…

Chi-square tests based on maximum likelihood (ML) estimation of covariance structures often incorrectly over-reject the null hypothesis: [sigma] = [sigma(theta)] when the sample size is small. Reweighted least squares (RLS) avoids this problem. In some models, the vector of parameter must contain means, variances, and covariances, yet whether RLS…

Measuring change in an educational or psychological construct over time is often achieved by repeatedly administering the same items to the same examinees over time and fitting a second-order latent growth curve model. However, latent growth modeling with full information maximum likelihood (FIML) estimation becomes computationally challenging…

A mixture extension of Samejima's continuous response model for continuous measurement outcomes and its estimation through a heuristic approach based on limited-information factor analysis is introduced. Using an empirical data set, it is shown that two groups of respondents that differ both qualitatively and quantitatively in their response…

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…

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…

Traditional IRT characteristic curve linking methods ignore parameter estimation errors, which may undermine the accuracy of estimated linking constants. Two new linking methods are proposed that take into account parameter estimation errors. The item- (IWCC) and test-information-weighted characteristic curve (TWCC) methods employ weighting…

Likert-type item is the most popular response format for collecting data in social, educational, and psychological studies through scales or questionnaires. However, there is no consensus on whether parametric or non-parametric tests should be preferred when analyzing Likert-type data. This study examined the statistical power of parametric and…

A simulation study was conducted to explore the impact of differential item functioning (DIF) on general factor difference estimation for bifactor, ordinal data. Common analysis misspecifications in which the generated bifactor data with DIF were fitted using models with equality constraints on noninvariant item parameters were compared under data…

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…

The aim of the study was to examine the common items in the mixed format (e.g., multiple-choices and essay items) contain parameter drifts in the test equating processes performed with the common item nonequivalent groups design. In this study, which was carried out using Monte Carlo simulation with a fully crossed design, the factors of test…