This review introduces classical item response theory (IRT) models as well as more
contemporary extensions to the case of multilevel, multidimensional, and mixtures of …

The fit of cognitive diagnostic models (CDMs) to response data needs to be evaluated, since
CDMs might yield misleading results when they do not fit the data well. Limited-information …

The goodness of fit (GOF) of a statistical model, such as an item response theory (IRT)
model, describes how well the model matches a set of observations. It is useful to distinguish …

Crafting a validity argument is crucial for the development of any assessment of ICT literacy.
In about the context of studying gender differences in ICT literacy, it has therefore become …

Two new methods to estimate the asymptotic covariance matrix for marginal maximum
likelihood estimation of cognitive diagnosis models (CDM s), the inverse of the observed …

Generalized fiducial inference (GFI) has been proposed as an alternative to likelihood-
based and Bayesian inference in mainstream statistics. Confidence intervals (CIs) can be …

Researchers who evaluate the fit of psychometric models to binary or multinomial items
often look at univariate and bivariate residuals to determine how a poorly fitting model can …

In item response theory (IRT), it is often necessary to perform restricted recalibration (RR) of
the model: A set of (focal) parameters is estimated holding a set of (nuisance) parameters …

In this manuscript, the applicability of the Hausman test to the evaluation of item response
models is investigated. The Hausman test is a general test of model fit. The test assesses …

This tutorial introduces the graded response model (GRM), a tool for testing measurement
precision within the item response theory (IRT) paradigm, which is useful for informing …