The reliability of a test score is usually underestimated and the deflation may be profound, 0.40 - 0.60 units of reliability or 46 - 71%. Eight root sources of the deflation are discussed and quantified by a simulation with 1,440 real-world datasets: (1) errors in the measurement modelling, (2) inefficiency in the estimator of reliability within…

Determining the number of factors in exploratory factor analysis (EFA) is crucial because it affects the rest of the analysis and the conclusions of the study. Researchers have developed various methods for deciding the number of factors to retain in EFA, but this remains one of the most difficult decisions in the EFA. The purpose of this study is…

This study utilizes an analysis of diminishing returns to examine the relationship between sample size and item parameter estimation precision when utilizing the Masters' Partial Credit Model for polytomous items. Item data from the standardization of the Batelle Developmental Inventory, 3rd Edition were used. Each item was scored with a…

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…

This study aims to analyze the differential bundle functioning in multidimensional tests with a specific purpose to detect this effect through differentiating the location of the item with DIF in the test, the correlation between the dimensions, the sample size, and the ratio of reference to focal group size. The first 10 items of the test that is…

Item parameter drift (IPD) is the systematic differentiation of parameter values of items over time due to various reasons. If it occurs in computer adaptive tests (CAT), it causes errors in the estimation of item and ability parameters. Identification of the underlying conditions of this situation in CAT is important for estimating item and…

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…

Iteration number in Monte Carlo simulation method used commonly in educational research has an effect on Item Response Theory test and item parameters. The related studies show that the number of iteration is at the discretion of the researcher. Similarly, there is no specific number suggested for the number of iteration in the related literature.…

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…

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…

Traditional psychometric guidelines suggest that at least several hundred respondents are needed to obtain accurate parameter estimates under the Rasch model. However, recent research indicates that Rasch equating results in accurate parameter estimates with sample sizes as small as 25. Item parameter drift under the Rasch model has been…

The aim of this study was to compare, by simulation, the accuracy of mapping a cut-score from one test to another by expert judgement (using the Angoff method) versus the accuracy with a small-sample equating method (chained linear equating). As expected, the standard-setting method resulted in more accurate equating when we assumed a higher level…

A log-linear model (LLM) is a well-known statistical method to examine the relationship among categorical variables. This study investigated the performance of LLM in detecting differential item functioning (DIF) for polytomously scored items via simulations where various sample sizes, ability mean differences (impact), and DIF types were…