Computing maximum likelihood estimates of loglinear models from marginal sums with special attention to loglinear item response theory

Marginal Maximum Likelihood Estimation of Item Response Models in R

Item response theory (IRT) models are a class of statistical models used by researchers to describe the response behaviors of individuals to a set of categorically scored items. The most common IRT models can be classified as generalized linear fixedand/or mixed-effect models. Although IRT models appear most often in the psychological testing literature, researchers in other fields have success...

Item Bias Detection Using Loglinear Irt

A method is proposed for the detection of item bias with respect to observed or unobserved subgroups. The method uses quasi-loglinear models for the incomplete subgroup x test score x Item 1 × • • • x item k contingency table. If subgroup membership is unknown the models are Haberman's incomplete-latent-class models. The (conditional) Rasch model is formulated as a quasi-loglinear model. The pa...

Links between Binary and Multi-category Logit Item Response Models and Quasi-symmetric Loglinear Models – 443 –

— Caussinus’s loglinear model of quasi symmetry has interesting connections with models for within-subject effects with repeated categorical measurement. For binary responses, Tjur (1982) showed that estimates of main effect parameters in the quasi-symmetry model are also conditional maximum likelihood estimates of item parameters for a fixed effects treatment of subject terms in the Rasch item...

Links Between Binary and Multi-Category Logit Item Response Models and Quasi-Symmetric Loglinear Models

Caussinus’s loglinear model of quasi symmetry has interesting connections with models for within-subject effects with repeated categorical measurement. For binary responses, Tjur (1982) showed that estimates of main effect parameters in the quasi-symmetry model are also conditional maximum likelihood estimates of item parameters for a fixed effects treatment of subject terms in the Rasch item r...

Negative Binomial Loglinear Mixed Models