Background/purpose: This study aimed to reveal the accuracy of estimation of multiple-choice test items parameters following the models of the item-response theory in measurement. Materials/methods: The researchers depended on the measurement accuracy indicators, which express the absolute difference between the estimated and actual values of the…

The focus of this paper is on the empirical relationship between item difficulty and item discrimination. Two studies--an empirical investigation and a simulation study--were conducted to examine the association between item difficulty and item discrimination under classical test theory and item response theory (IRT), and the effects of the…

A key consideration when giving any computerized adaptive test (CAT) is how much adaptation is present when the test is used in practice. This study introduces a new framework to measure the amount of adaptation of Rasch-based CATs based on looking at the differences between the selected item locations (Rasch item difficulty parameters) of the…

The Rasch model is commonly used to calibrate multiple choice items. However, the sample sizes needed to estimate the Rasch model can be difficult to attain (e.g., consider a small testing company trying to pretest new items). With small sample sizes, auxiliary information besides the item responses may improve estimation of the item parameters.…

This study aims to examine the effects of mixture item response theory (IRT) models on item parameter estimation and classification accuracy under different conditions. The manipulated variables of the simulation study are set as mixture IRT models (Rasch, 2PL, 3PL); sample size (600, 1000); the number of items (10, 30); the number of latent…

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 study examined the use of Bayesian analysis methods for the estimation of item parameters in a two-parameter logistic item response theory model. Using simulated data under various design conditions with both informative and non-informative priors, the parameter recovery of Bayesian analysis methods were examined. Overall results showed that…

Studies have shown that item difficulty can vary significantly based on the context of an item within a test form. In particular, item position may be associated with practice and fatigue effects that influence item parameter estimation. The purpose of this research was to examine the relevance of item position specifically for assessments used in…

Although content validity--how well each item of an instrument represents the construct being measured--is foundational in the development of an instrument, statistical validity is also important to the decisions that are made based on the instrument. The primary purpose of this study is to demonstrate how simulation studies can be used to assist…

The equating performance of two internal anchor test structures--miditests and minitests--is studied for four IRT equating methods using simulated data. Originally proposed by Sinharay and Holland, miditests are anchors that have the same mean difficulty as the overall test but less variance in item difficulties. Four popular IRT equating methods…

When constructing multiple test forms, the number of items and the total test difficulty are often equivalent. Not all test developers match the number of items and/or average item difficulty within subcontent areas. In this simulation study, six test forms were constructed having an equal number of items and average item difficulty overall.…

The aim of this simulation study, determine the relationship between true latent scores and estimated latent scores by including various control variables and different statistical models. The study also aimed to compare the statistical models and determine the effects of different distribution types, response formats and sample sizes on latent…

This study compares the performance of two estimation algorithms of new usage, the Metropolis-Hastings Robins-Monro (MHRM) and the Hamiltonian MCMC (HMC), with two consolidated algorithms in the psychometric literature, the marginal likelihood via EM algorithm (MML-EM) and the Markov chain Monte Carlo (MCMC), in the estimation of multidimensional…

A new variant of the iterative "data = fit + residual" data-analytical approach described by Mosteller and Tukey is proposed and implemented in the context of item response theory psychometric models. Posterior probabilities from a Bayesian mixture model of a Rasch item response theory model and an unscalable latent class are expressed…

In common-item equating the anchor block is generally built to represent a miniature form of the total test in terms of content and statistical specifications. The statistical properties frequently reflect equal mean and spread of item difficulty. Sinharay and Holland (2007) suggested that the requirement for equal spread of difficulty may be too…