This article studies the Type I error, false positive rates, and power of four versions of the Lagrange multiplier test to detect measurement noninvariance in item response theory (IRT) models for binary data under model misspecification. The tests considered are the Lagrange multiplier test computed with the Hessian and cross-product approach,…

Viable methods for the identification of item misfit or Differential Item Functioning (DIF) are central to scale construction and sound measurement. Many approaches rely on the derivation of a limiting distribution under the assumption that a certain model fits the data perfectly. Typical DIF assumptions such as the monotonicity and population…

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…

Simulations concerning the distributional assumptions of coefficient alpha are contradictory. To provide a more principled theoretical framework, this article relies on the Fréchet-Hoeffding bounds, in order to showcase that the distribution of the items play a role on the estimation of correlations and covariances. More specifically, these bounds…

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 performance of the normal theory bootstrap (NTB), the percentile bootstrap (PB), and the bias-corrected and accelerated (BCa) bootstrap confidence intervals (CIs) for coefficient omega was assessed through a Monte Carlo simulation under conditions not previously investigated. Of particular interests were nonnormal Likert-type and binary items.…

Typically a longitudinal growth modeling based on item response theory (IRT) requires repeated measures data from a single group with the same test design. If operational or item exposure problems are present, the same test may not be employed to collect data for longitudinal analyses and tests at multiple time points are constructed with unique…

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…

This study reports results of an investigation based on simulated data of the distributional properties of the item fit statistics that are commonly used in the Rasch model calibration programs as indices of the fit of responses to individual items to the measurement model. (SLD)

Simulated data are used to assess the appropriateness of using separate calibration and between-fit approaches to detecting item bias in the Rasch rating scale model. Results indicate that Type I error rates for the null distribution hold even when there are different ability levels for reference and focal groups. (SLD)

Effects of the following variables on performance of computerized adaptive testing (CAT) procedures for the partial credit model (PCM) were studied: (1) stopping rule for terminating CAT; (2) item pool size; and (3) distribution of item difficulties. Implications of findings for CAT systems based on the PCM are discussed. (SLD)

Monte Carlo techniques are used to examine the power of the "B" statistic of R. L. Brennan (1972) to detect negatively discriminating items drawn from a variety of nonnormal population distributions. A simplified procedure is offered for conducting an item-discrimination analysis on typical classroom objective tests. (SLD)