Simultaneous Estimation of Multinomial Logistic Regression Models: Factor Analysis of Polytomous Item Response Data with Covariates

The approach described in this talk starts with Bock's (1972) nominal response model (NRM). The NRM is a multinomial logistic regression model for responses to items where the ordering of response options is not known a priori and the predictor or explanatory variable is unobserved (i.e., the latent construct). The latent variable in the multinomial logistic regression is replaced with an estimate based on responses to all other items. Given a set of items, there is one multinomial logistic regression for each. The problem then becomes one of simultaneously estimating multinomial logistic regressions with restrictions across the models. This approach allows us to go beyond what is typical in standard item response theory modeling in that we can handle multiple correlated latent constructs, impose (linear and/or ordinal) restrictions on category scores, test the effect of additional variables (e.g., a treatment versus control condition), create hybrid IRT models, and obtain measures on the latent constructs. An extension of the approach will also be described that is akin to a structural equation model for observed discrete data.