A Multinomial Framework for Ideal Point Estimation

This paper creates a multinomial framework for ideal point estimation (mIRT) using recent developments in Bayesian statistics. The core model relies on a flexible multinomial specification that includes most common models in political science as “special cases.†I show that popular extensions (e.g., dynamic smoothing, inclusion of covariates, and network models) can be easily incorporated whilst maintaining the ability to estimate a model using a Gibbs Sampler or exact EM algorithm. By showing that these models can be written and estimated using a shared framework, the paper aims to reduce the proliferation of bespoke ideal point models as well as extend the ability of applied researchers to estimate models quickly using the EM algorithm. I apply this framework to a thorny question in scaling survey responses—the treatment of nonresponse. Focusing on the American National Election Study (ANES), I suggest that a simple but principled solution is to treat questions as multinomial where nonresponse is a distinct (modeled) category. The exploratory results suggest that certain questions tend to attract many more invalid answers and that many of these questions (particularly when signaling out particular social groups for evaluation) are masking noncentrist (typically conservative) beliefs.