The main purpose of this study is to examine the Type I error and statistical power ratios of Differential Item Functioning (DIF) techniques based on different theories under different conditions. For this purpose, a simulation study was conducted by using Mantel-Haenszel (MH), Logistic Regression (LR), Lord's [chi-squared], and Raju's Areas…

To reduce the impact of parameter estimation errors on IRT linking results, recent work introduced two information-weighted characteristic curve methods for dichotomous items. These two methods showed outstanding performance in both simulation and pseudo-form pseudo-group analysis. The current study expands upon the concept of information…

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…

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…

Differential item functioning (DIF) is often used to examine validity evidence of alternate form test accommodations. Unfortunately, traditional approaches for evaluating DIF are prone to selection bias. This article proposes a novel DIF framework that capitalizes on regression discontinuity design analysis to control for selection bias. A…

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…

Two families of analysis methods can be used for differential item functioning (DIF) analysis. One family is DIF analysis based on observed scores, such as the Mantel-Haenszel (MH) and the standardized proportion-correct metric for DIF procedures; the other is analysis based on latent ability, in which the statistic is a measure of departure from…

This Monte Carlo simulation study aimed to investigate confirmatory factor analysis (CFA) estimation methods under different conditions, such as sample size, distribution of indicators, test length, average factor loading, and factor structure. Binary data were generated to compare the performance of maximum likelihood (ML), mean and variance…

Weighted least squares (WLS), weighted least squares mean-and-variance-adjusted (WLSMV), unweighted least squares mean-and-variance-adjusted (ULSMV), maximum likelihood (ML), robust maximum likelihood (MLR) and Bayesian estimation methods were compared in mixed item response type data via Monte Carlo simulation. The percentage of polytomous items,…

When using the Rasch model, equating with a nonequivalent groups anchor test design is commonly achieved by adjustment of new form item difficulty using an additive equating constant. Using simulated 5-year data, this report compares 4 approaches to calculating the equating constants and the subsequent impact on equating results. The 4 approaches…

This study examined the performance of a proposed iterative Wald approach for detecting differential item functioning (DIF) between two groups when preknowledge of anchor items is absent. The iterative approach utilizes the Wald-2 approach to identify anchor items and then iteratively tests for DIF items with the Wald-1 approach. Monte Carlo…

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…

In observed-score equipercentile equating, the goal is to make scores on two scales or tests measuring the same construct comparable by matching the percentiles of the respective score distributions. If the tests consist of different items with multiple categories for each item, a suitable model for the responses is a polytomous item response…

This study analysed polytomous items' psychometric properties according to nonparametric item response theory (NIRT) models. Thus, simulated datasets--three different test lengths (10, 20 and 30 items), three sample distributions (normal, right and left skewed) and three samples sizes (100, 250 and 500)--were generated by conducting 20…

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…