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…

For efficiency, Computerized Adaptive Test (CAT) algorithm selects items with the maximum information, typically with a 50% probability of being answered correctly. However, examinees may not be satisfied if they only correctly answer 50% of the items. Researchers discovered that changing the item selection algorithms to choose easier items (i.e.,…

Recently, adaptive test approaches have become a viable alternative to traditional fixed-item tests. The main advantage of adaptive tests is that they reach desired measurement precision with fewer items. However, fewer items mean that each item has a more significant effect on ability estimation and therefore those tests are open to more…

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…

Testlets bring several perks in the development and administration of tests, such as 1) the construction of meaningful test items, 2) the avoidance of non-relevant context exposure, 3) the improvement of testing efficiency, and 4) the progression of testlet items requiring higher thinking skills. Thus, the inclusion of testlets in educational…

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…

The present paper introduces a general multidimensional model to measure individual differences in learning within a single administration of a test. Learning is assumed to result from practicing the operations involved in solving the items. The model accounts for the possibility that the ability to learn may manifest differently for correct and…

In this digital ITEMS module, Dr. Brian Leventhal and Dr. Allison Ames provide an overview of "Monte Carlo simulation studies" (MCSS) in "item response theory" (IRT). MCSS are utilized for a variety of reasons, one of the most compelling being that they can be used when analytic solutions are impractical or nonexistent because…

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…

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.…

Longitudinal models of individual growth typically emphasize between-person predictors of change but ignore how growth may vary "within" persons because each person contributes only one point at each time to the model. In contrast, modeling growth with multi-item assessments allows evaluation of how relative item performance may shift…

Longitudinal models typically emphasize between-person predictors of change but ignore how growth varies "within" persons because each person contributes only one data point at each time. In contrast, modeling growth with multi-item assessments allows evaluation of how relative item performance may shift over time. While traditionally…

Many scholars compared various item discrimination indices in real or simulated data. Item discrimination indices, such as item-total correlation, item-rest correlation, and IRT item discrimination parameter, provide information about individual differences among all participants. However, there are tests that aim to select a very limited number…

Response time models (RTMs) are of increasing interest in educational and psychological testing. This article focuses on the lognormal model for response times, which is one of the most popular RTMs. Several existing statistics for testing normality and the fit of factor analysis models are repurposed for testing the fit of the lognormal model. A…