Logit Models and Related Quasi-Symmetric Log-Linear Models for Comparing Responses to Similar Items in a Survey

Abstract

Suppose that subjects respond to a battery of questions (items) of a similar nature in a survey, with each item having the same categorical scale. This article discusses models that express logits for the response distributions in terms of subject and item effects. The models, which generalize the Rasch model, have interpretations referring to subject-specific comparisons of the items. Recent literature shows that one can estimate item parameters using estimates of main effect parameters in corresponding quasi-symmetric log-linear models. We discuss this connection, giving primary attention to ordinal-response models using adjacent-category logits and cumulative logits. For the case of two items, we give expressions for models and corresponding parameter estimates that are the basis of simple tests of marginal homogeneity for square ordinal contingency tables.