Latent Dirichlet Analysis of Categorical Survey Responses

TL;DR

This paper introduces a Bayesian hierarchical latent class model to analyze categorical survey responses, revealing hidden belief structures and heterogeneity, with applications in economic behavior and sentiment analysis.

Contribution

It develops a novel Bayesian hierarchical latent class model for categorical survey data, linking it to economic theory and providing an estimation algorithm for dynamic responses.

Findings

Survey responses contain additional information beyond published indices.

Belief types can be used to estimate heterogeneous returns to education.

The model captures comovements and heterogeneity in beliefs across individuals.

Abstract

Beliefs are important determinants of an individual's choices and economic outcomes, so understanding how they comove and differ across individuals is of considerable interest. Researchers often rely on surveys that report individual beliefs as qualitative data. We propose using a Bayesian hierarchical latent class model to analyze the comovements and observed heterogeneity in categorical survey responses. We show that the statistical model corresponds to an economic structural model of information acquisition, which guides interpretation and estimation of the model parameters. An algorithm based on stochastic optimization is proposed to estimate a model for repeated surveys when responses follow a dynamic structure and conjugate priors are not appropriate. Guidance on selecting the number of belief types is also provided. Two examples are considered. The first shows that there is information in the Michigan survey responses beyond the consumer sentiment index that is officially published. The second shows that belief types constructed from survey responses can be used in a subsequent analysis to estimate heterogeneous returns to education.