Building on previous works by Lord and Ogasawara for dichotomous items, this article proposes an approach to derive the asymptotic standard errors of item response theory true score equating involving polytomous items, for equivalent and nonequivalent groups of examinees. This analytical approach could be used in place of empirical methods like…

We investigate the current bandwidth selection methods in kernel equating and propose a method based on Silverman's rule of thumb for selecting the bandwidth parameters. In kernel equating, the bandwidth parameters have previously been obtained by minimizing a penalty function. This minimization process has been criticized by practitioners…

This article used the Wald test to evaluate the item-level fit of a saturated cognitive diagnosis model (CDM) relative to the fits of the reduced models it subsumes. A simulation study was carried out to examine the Type I error and power of the Wald test in the context of the G-DINA model. Results show that when the sample size is small and a…

This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…

The applications of item response theory (IRT) models assume local item independence and that examinees are independent of each other. When a representative sample for psychometric analysis is selected using a cluster sampling method in a testlet-based assessment, both local item dependence and local person dependence are likely to be induced.…

In the nonequivalent groups with anchor test (NEAT) design, the standard error of linear observed-score equating is commonly estimated by an estimator derived assuming multivariate normality. However, real data are seldom normally distributed, causing this normal estimator to be inconsistent. A general estimator, which does not rely on the…

Successful administration of computerized adaptive testing (CAT) programs in educational settings requires that test security and item exposure control issues be taken seriously. Developing an item selection algorithm that strikes the right balance between test precision and level of item pool utilization is the key to successful implementation…

Tucker and chained linear equatings were evaluated in two testing scenarios. In Scenario 1, referred to as rater comparability scoring and equating, the anchor-to-total correlation is often very high for the new form but moderate for the reference form. This may adversely affect the results of Tucker equating, especially if the new and reference…

This study investigated differences between two approaches to chained equipercentile (CE) equating (one- and bi-direction CE equating) in nearly equal groups and relatively unequal groups. In one-direction CE equating, the new form is linked to the anchor in one sample of examinees and the anchor is linked to the reference form in the other…

Growth models are used extensively in the context of educational accountability to evaluate student-, class-, and school-level growth. However, when error-prone test scores are used as independent variables or right-hand-side controls, the estimation of such growth models can be substantially biased. This article introduces a…

The focus of this paper is assessing the impact of measurement errors on the prediction error of an observed-score regression. Measures are presented and described for decomposing the linear regression's prediction error variance into parts attributable to the true score variance and the error variances of the dependent variable and the predictor…

Although a few studies report sizable score gains for examinees who repeat performance-based assessments, research has not yet addressed the reliability and validity of inferences based on ratings of repeat examinees on such tests. This study analyzed scores for 8,457 single-take examinees and 4,030 repeat examinees who completed a 6-hour clinical…

Errors don't exist in our data, but they serve a vital function. Reality is complicated, but our models need to be simple in order to be manageable. We assume that attributes are invariant over some conditions of observation, and once we do that we need some way of accounting for the variability in observed scores over these conditions of…

The impact of log-linear presmoothing on the accuracy of small sample chained equipercentile equating was evaluated under two conditions. In the first condition the small samples differed randomly in ability from the target population. In the second condition the small samples were systematically different from the target population. Results…

Research has often found that, when high school grades and SAT scores are used to predict first-year college grade-point average (FGPA) via regression analysis, African-American and Latino students, are, on average, predicted to earn higher FGPAs than they actually do. Under various plausible models, this phenomenon can be explained in terms of…