We discuss an application of Bayesian factor analysis for estimation of the optimal linear combination and associated maximal reliability of a multi-component measuring instrument. The described procedure yields point and credibility interval estimates of this reliability coefficient, which are readily obtained in educational and behavioral…

This article presents generalizations of SIBTEST and crossing-SIBTEST statistics for differential item functioning (DIF) investigations involving more than two groups. After reviewing the original two-group setup for these statistics, a set of multigroup generalizations that support contrast matrices for joint tests of DIF are presented. To…

We illustrate how to analyze complete generalizability theory (GT) designs using structural equation modeling software ("lavaan" in R), compare results to those obtained from numerous ANOVA-based packages, and apply those results in practical ways using data obtained from a large sample of respondents, who completed the Self-Perception…

To reduce the impact of parameter estimation errors on IRT linking results, recent work introduced two information-weighted characteristic curve methods for dichotomous items. These two methods showed outstanding performance in both simulation and pseudo-form pseudo-group analysis. The current study expands upon the concept of information…

Much research has been devoted to identification of differential item functioning (DIF), which occurs when the item responses for individuals from two groups differ after they are conditioned on the latent trait being measured by the scale. There has been less work examining differential step functioning (DSF), which is present for polytomous…

This article presents the performance of item response theory (IRT) models when double ratings are used as item scores over single ratings when rater effects are present. Study 1 examined the influence of the number of ratings on the accuracy of proficiency estimation in the generalized partial credit model (GPCM). Study 2 compared the accuracy of…

Testing item fit is central in item response theory (IRT) modeling, since a good fit is necessary to draw valid inferences from estimated model parameters. "Infit" and "outfit" fit statistics, widespread indices for detecting deviations from the Rasch model, are affected by data factors, such as sample size. Consequently, the…

This study evaluates various scoring methods including number-correct scoring, IRT theta scoring, and hybrid scoring in terms of scale-score stability over time. A simulation study was conducted to examine the relative performance of five scoring methods in terms of preserving the first two moments of scale scores for a population in a chain of…

During the development of large-scale school achievement tests, panels of independent subject-matter experts use systematic judgmental methods to rate the correspondence between a given test's items and performance objective statements. The individual experts' ratings may then be used to compute summary indices to quantify the match between a…

Recent research has suggested that re-setting the standard for each administration of a small sample examination, in addition to the high cost, does not adequately maintain similar performance expectations year after year. Small-sample equating methods have shown promise with samples between 20 and 30. For groups that have fewer than 20 students,…

The characteristic curve methods have been applied to estimate the equating coefficients in test equating under the graded response model (GRM). However, the approaches for obtaining the standard errors for the estimates of these coefficients have not been developed and examined. In this study, the delta method was applied to derive the…

Longitudinal models typically emphasize between-person predictors of change but ignore how growth varies "within" persons because each person contributes only one data point at each time. In contrast, modeling growth with multi-item assessments allows evaluation of how relative item performance may shift over time. While traditionally…

Traditional psychometric guidelines suggest that at least several hundred respondents are needed to obtain accurate parameter estimates under the Rasch model. However, recent research indicates that Rasch equating results in accurate parameter estimates with sample sizes as small as 25. Item parameter drift under the Rasch model has been…

When there are no personal consequences associated with test performance for examinees, rapid guessing (RG) is a concern and can differ between subgroups. To date, the impact of differential RG on item-level measurement invariance has received minimal attention. To that end, a simulation study was conducted to examine the robustness of the…

The usefulness of item response theory (IRT) models depends, in large part, on the accuracy of item and person parameter estimates. For the standard 3 parameter logistic model, for example, these parameters include the item parameters of difficulty, discrimination, and pseudo-chance, as well as the person ability parameter. Several factors impact…