The unstructured multiple-attempt (MA) item response data in virtual learning environments (VLEs) are often from student-selected assessment data sets, which include missing data, single-attempt responses, multiple-attempt responses, and unknown growth ability across attempts, leading to a complex and complicated scenario for using this kind of…

The aim of this study was to examine the precision of item parameter estimation in different sample sizes and test lengths under three parameter logistic model (3PL) item response theory (IRT) model, where the trait measured by a test was not normally distributed or had a skewed distribution. In the study, number of categories (1-0), and item…

Mixture Rasch (MixRasch) models conventionally assume normal distributions for latent ability. Previous research has shown that the assumption of normality is often unmet in educational and psychological measurement. When normality is assumed, asymmetry in the actual latent ability distribution has been shown to result in extraction of spurious…

The current study investigated the impact of matching criterion purification on the accuracy of differential item functioning (DIF) detection in large-scale assessments. The three matching approaches for DIF analyses (block-level matching, pooled booklet matching, and equated pooled booklet matching) were employed with the Mantel-Haenszel…

Simulations were conducted to examine the effect of differential item functioning (DIF) on measurement consequences such as total scores, item response theory (IRT) ability estimates, and test reliability in terms of the ratio of true-score variance to observed-score variance and the standard error of estimation for the IRT ability parameter. The…

As item response theory has been more widely applied, investigating the fit of a parametric model becomes an important part of the measurement process. There is a lack of promising solutions to the detection of model misfit in IRT. Douglas and Cohen introduced a general nonparametric approach, RISE (Root Integrated Squared Error), for detecting…

This simulation study compared the performances (Type I error and power) of Mantel-Haenszel (MH), SIBTEST, and item response theory-likelihood ratio (IRT-LR) methods under certain conditions. Manipulated factors were sample size, ability differences between groups, test length, the percentage of differential item functioning (DIF), and underlying…

Compared differential item functioning detection rates for logistic regression and analysis of variance for dichotomously scored items using simulated data and varying test length, sample size, discrimination rate, and underlying ability. Explains why the logistic regression method is recommended for most applications. (SLD)

Hierarchical Bayes procedures for the two-parameter logistic item response model were compared for estimating item and ability parameters through two joint and two marginal Bayesian procedures. Marginal procedures yielded smaller root mean square differences for item and ability, but results for larger sample size and test length were similar.…

The Mantel-Haenszel (MH) statistic for identifying differential item functioning (DIF) commonly conditions on the observed test score as a surrogate for conditioning on latent ability. When the comparison group distributions are not completely overlapping (i.e., are incongruent), the observed score represents different levels of latent ability…

The accuracy of estimation procedures in item response theory was studied using Monte Carlo methods and varying sample size, number of subjects, and distribution of ability parameters for: (1) joint maximum likelihood as implemented in the computer program LOGIST; (2) marginal maximum likelihood; and (3) marginal Bayesian procedures as implemented…

The power of the procedure of W. Stout to detect deviations from essential unidimensionality in two-dimensional data was investigated for minor, moderate, and large deviations from unidimensionality using criteria for deviations from unidimensionality based on prior research. Test lengths of 20 and 40 items and sample sizes of 700 and 1,500 were…

This study was designed to compare the accuracy of three commonly used ability estimation procedures under the graded response model. The three methods, maximum likelihood (ML), expected a posteriori (EAP), and maximum a posteriori (MAP), were compared using a recovery study design for two sample sizes, two underlying ability distributions, and…

DIMTEST is a statistical test procedure for assessing essential unidimensionality of binary test item responses. The test statistic T used for testing the null hypothesis of essential unidimensionality is a nonparametric statistic. That is, there is no particular parametric distribution assumed for the underlying ability distribution or for the…

Hierarchical Bayes procedures were compared for estimating item and ability parameters in item response theory. Simulated data sets from the two-parameter logistic model were analyzed using three different hierarchical Bayes procedures: (1) the joint Bayesian with known hyperparameters (JB1); (2) the joint Bayesian with information hyperpriors…