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…

In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…

This study linked nonlinear profile analysis (NPA) of dichotomous responses with an existing family of item response theory models and generalized latent variable models (GLVM). The NPA method offers several benefits over previous internal profile analysis methods: (a) NPA is estimated with maximum likelihood in a GLVM framework rather than…

An evaluation of the variation of item estimates was conducted for the multidimensional extension of the logistic item response theory (MIRT) model. The empirically determined standard errors (SEs) of marginal maximum likelihood estimation (MMLE)/Bayesian item estimates from 40 items from the ACT Assessment (Form 24b, 1985) were obtained when the…

The analytically derived asymptotic standard errors (SEs) of maximum likelihood (ML) item estimates can be approximated by a mathematical function without examinees' responses to test items, and the empirically determined SEs of marginal maximum likelihood estimation (MMLE)/Bayesian item estimates can be obtained when the same set of items is…

Measurement disturbances, such as guessing, startup, and plodding, often result in an examinee's ability being either over- or under-estimated by the maximum likelihood estimation employed in latent trait psychometric models. Several authors have suggested methods to lessen the impact of unexpected responses on the ability estimation process. This…

An experiment was performed with computer-generated data to investigate some of the operational characteristics of tailored testing as they are related to various provisions of the computer program and item pool. With respect to the computer program, two characteristics were varied: the size of the step of increase or decrease in item difficulty…