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,…

This article illustrates five different methods for estimating Angoff cut scores using item response theory (IRT) models. These include maximum likelihood (ML), expected a priori (EAP), modal a priori (MAP), and weighted maximum likelihood (WML) estimators, as well as the most commonly used approach based on translating ratings through the test…

Cross-level invariance in a multilevel item response model can be investigated by testing whether the within-level item discriminations are equal to the between-level item discriminations. Testing the cross-level invariance assumption is important to understand constructs in multilevel data. However, in most multilevel item response model…

Different estimation procedures have been developed for the unidimensional three-parameter item response theory (IRT) model. These techniques include the marginal maximum likelihood estimation, the fully Bayesian estimation using Markov chain Monte Carlo simulation techniques, and the Metropolis-Hastings Robbin-Monro estimation. With each…

Standard approaches for estimating item response theory (IRT) model parameters generally work under the assumption that the latent trait being measured by a set of items follows the normal distribution. Estimation of IRT parameters in the presence of nonnormal latent traits has been shown to generate biased person and item parameter estimates. A…

The aim of this study is to determine variance difference between maximum likelihood and expected A posteriori estimation methods viewed from number of test items of aptitude test. The variance presents an accuracy generated by both maximum likelihood and Bayes estimation methods. The test consists of three subtests, each with 40 multiple-choice…

Testlets, or groups of related items, are commonly included in educational assessments due to their many logistical and conceptual advantages. Despite their advantages, testlets introduce complications into the theory and practice of educational measurement. Responses to items within a testlet tend to be correlated even after controlling for…

A simulation study was conducted to explore the performance of the linear logistic test model (LLTM) when the relationships between items and cognitive components were misspecified. Factors manipulated included percent of misspecification (0%, 1%, 5%, 10%, and 15%), form of misspecification (under-specification, balanced misspecification, and…

In this study we compared five item selection procedures using three ability estimation methods in the context of a mixed-format adaptive test based on the generalized partial credit model. The item selection procedures used were maximum posterior weighted information, maximum expected information, maximum posterior weighted Kullback-Leibler…

For computerized adaptive tests (CATs) to work well, they must have an item pool with sufficient numbers of good quality items. Many researchers have pointed out that, in developing item pools for CATs, not only is the item pool size important but also the distribution of item parameters and practical considerations such as content distribution…

The usefulness of the l[subscript z] person-fit index was investigated with achievement test data from 20 exams given to more than 3,200 college students. Results for three methods of estimating ? showed that the distributions of l[subscript z] were not consistent with its theoretical distribution, resulting in general overfit to the item response…

In administration of individually administered intelligence tests, items are commonly presented in a sequence of increasing difficulty, and test administration is terminated after a predetermined number of incorrect answers. This practice produces stochastically censored data, a form of nonignorable missing data. By manipulating four factors…

This paper describes and evaluates the use of measurement decision theory (MDT) to classify examinees based on their item response patterns. The model has a simple framework that starts with the conditional probabilities of examinees in each category or mastery state responding correctly to each item. The presented evaluation investigates: (1) the…

Hierarchical Bayes procedures for the two-parameter logistic item response model were compared for estimating item parameters. Simulated data sets were analyzed using two different Bayes estimation procedures, the two-stage hierarchical Bayes estimation (HB2) and the marginal Bayesian with known hyperparameters (MB), and marginal maximum…

Maximum likelihood and Bayesian estimates of proficiency, typically used in adaptive testing, use item weights that depend on test taker proficiency to estimate test taker proficiency. In this study, several methods were explored through computer simulation using fixed item weights, which depend mainly on the items difficulty. The simpler scores…