Hierarchical Item Response Models for Analyzing Public Opinion

• In Event: 3269 - Statistical Advances

Abstract

Opinion surveys typically employ multiple items to measure values, beliefs, or attitudes toward a particular issue (e.g., abortion) or in a broadly defined issue domain (e.g., racial attitudes). To examine how individual and contextual characteristics predict opinion, researchers have either adopted a one-item-at-a-time approach, i.e., fitting a generalized linear model for each item, or followed a two-step approach by constructing a composite measure on which subsequent analyses are based. In this paper, I present a class of hierarchical item response theory (IRT) models that can be fruitfully applied to analyze public opinion data. In this approach, individual responses to multiple items result from a latent preference that follows a normal prior, in which both the mean and the variance may depend on observed covariates. Compared with the one-item-at-a-time approach, it pools information from multiple items, thus increasing statistical power. Compared with the two-step approach, the embedding of a hierarchical structure into IRT allows us to jointly estimate the effects of individual covariates and item parameters. The joint estimation — via maximizing the marginal likelihood — is computationally fast, statistically efficient, and offers valid asymptotic inference of all parameters. Further, as I illustrate with data from the American National Election Studies (ANES), simultaneous modeling of the mean and the variance of individual preferences enables us not only to investigate how preferences differ among groups, vary across regions, or evolve over time, but also to identify levels, trends, and patterns of attitude polarization and ideological constraint, two recurring themes in public opinion research. An open source R package, hIRT, is available for fitting the proposed class of hierarchical IRT models.

Author

• Xiang Zhou, Harvard University