Summed Score Likelihood–Based Indices for Testing Latent Variable Distribution Fit in Item Response Theory

Diagnosing item score patterns on a test using item response theory-based person-fit statistics.

Person-fit statistics have been proposed to investigate the fit of an item score pattern to an item response theory (IRT) model. The author investigated how these statistics can be used to detect different types of misfit. Intelligence test data were analyzed using person-fit statistics in the context of the G. Rasch (1960) model and R. J. Mokken's (1971, 1997) IRT models. The effect of the cho...

Latent Variable Selection for Multidimensional Item Response Theory Models via L1 Regularization

We develop a latent variable selection method for multidimensional item response theory models. The proposed method identifies latent traits probed by items of a multidimensional test. Its basic strategy is to impose an L1 penalty term to the log-likelihood. The computation is carried out by the expectationmaximization algorithm combined with the coordinate descent algorithm. To the authors’ be...

ltm: An R Package for Latent Variable Modeling and Item Response Theory Analyses

The R package ltm has been developed for the analysis of multivariate dichotomous and polytomous data using latent variable models, under the Item Response Theory approach. For dichotomous data the Rasch, the Two-Parameter Logistic, and Birnbaum’s Three-Parameter models have been implemented, whereas for polytomous data Semejima’s Graded Response model is available. Parameter estimates are obta...

Limited-information goodness-of-fit testing of item response theory models for sparse 2 tables.

Bartholomew and Leung proposed a limited-information goodness-of-fit test statistic (Y) for models fitted to sparse 2(P ) contingency tables. The null distribution of Y was approximated using a chi-squared distribution by matching moments. The moments were derived under the assumption that the model parameters were known in advance and it was conjectured that the approximation would also be app...

Testing Parameter Invariance for Questionnaire Indices using Confirmatory Factor Analysis and Item Response Theory