An approximation procedure is proposed for the posterior means and standard deviation of the ability parameter in an item response model. The method is illustrated for the two-parameter logistic model using data from a 39-item American College Testing mathematics test. The effect of sample size is considered. (SLD)

The issue of person fit has received an increasing amount of attention by researchers in the past few years. Several studies have focused on the issue of how nonmodel-fitting responses affect the accuracy of ability estimates (e.g. R. Meijer and S. Nering, in press; Reise, 1995). The purpose of this study was to examine the effects that…

Investigated the effect of item parameter drift on ability estimates under item response theory, simulating item response data for two testing occasions for the two-parameter logistic model under several crossed conditions. Results show that item parameter drift under the simulated conditions had a small effect on ability estimates. (SLD)

Vocabulary fixed-item (FIT), computerized-adaptive (CAT), and self-adapted (SAT) tests were compared with 121 college students. CAT was more precise and efficient than SAT, which was more precise and efficient than FIT. SAT also yielded higher ability estimates for individuals with lower verbal self-concepts. (SLD)

In this study, the robustness of item parameter estimates with respect to the underlying distribution of abilities was explored. Using simulated datasets, item parameters were derived from a large sample representing the population versus samples representing a subset of ability and subsequently compared for possible mismatch. Comparisons were…

The situation of nonrandomly missing data has theoretically different implications for item parameter estimation depending on whether joint maximum likelihood or marginal maximum likelihood methods are used in the estimation. The objective of this paper is to illustrate what potentially can happen, under these estimation procedures, when there is…

It is not unusual for several tests measuring different abilities to be given in one test administration. A common practice is to estimate these abilities independently of each other, but this paper proposes a more efficient method of estimating these abilities that takes into account the correlational structure of the abilities. The method uses a…

Simulated items from two test forms using joint maximum likelihood estimation (JMLE) and marginal maximum likelihood estimation (MML) in the vertical equating situation (using an anchor test) when data were nonrandomly missing. Under MML, when the different ability parameters of students were not taken into account, the item difficulty parameters…

Develops an item-parameter estimation procedure using an EM algorithm for the continuous-response model (F. Samejima, 1973). Examines the usefulness of this model using simulated data. Results show that the procedure performs well in estimating items and theta parameters. (SLD)

Reviewed methods of estimating theta suitable for computerized adaptive testing (CAT) and discussed the differences between Fisher and Kullback-Leibler information criteria for selecting items. Examined the accuracy of different CAT algorithms using samples from the National Assessment of Educational Progress. Results show when correcting for…

It is a common practice in item response theory (IRT) to treat estimates of item parameters, say "B" circumflex, as if they were the known, true quantities, "B." However, ignoring the uncertainty associated with item parameters can lead to biases and over-confidence in subsequent inferences such as ability estimation,…

The purpose of this Monte Carlo study was to evaluate the relative accuracy of T. Warm's weighted likelihood estimate (WLE) compared to maximum likelihood estimate (MLE), expected a posteriori estimate (EAP), and maximum a posteriori estimate (MAP), using the generalized partial credit model (GPCM) and graded response model (GRM) under a variety…

The ability estimates of Gibbs sampling and the magnitudes of the posterior standard deviations were investigated. Item parameters of the Q-E intelligence test (J. Fraenkel and N. Wallen, 2000) for 44 examinees were obtained using Gibbs sampling, marginal Bayesian estimation, and BILOG. Two normal priors were used in item parameter estimation.…

The impact of missing data on estimates of gender differences in hierarchically ordered ability dimensions was studied using 13 ability tests taken by 1,224 13-year olds and 3 standardized achievement tests taken by 981 participants. Results indicate that analysis of missing data can contribute to understanding of gender differences. (SLD)

Explores the asymptotic theory of a method of nonparametric item characteristic curve estimation based on kernel smoothing with the theory of obtaining the proper linear ordering of examinees with respect to their true latent abilities. Results support the usefulness of estimates of the type produced by the TESTGRAF program. (SLD)