Latent Dirichlet Analysis of Categorical Survey Responses
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Data from surveys are increasingly available as the internet provides a new medium for conducting them. A typical survey consists of multiple questions, each with a menu of responses that are often categorical and qualitative in nature, and respondents are heterogeneous in both observed and unobserved ways. Existing methods that construct summary indices often ignore discreteness and do not provide adequately capture heterogeneity among individuals. We capture these features in a set of low dimensional latent variables using a Bayesian hierarchical latent class model that is adapted from probabilistic topic modeling of text data. An algorithm based on stochastic optimization is proposed to estimate a model for repeated surveys when conjugate priors are no longer available. Guidance on selecting the number of classes is also provided. The methodology is used in three applications, one to show how wealth indices can be constructed for developing countries where continuous data tend to be unreliable, and one to show that there is information in Michigan survey responses beyond the consumer sentiment index that is officially published. Using returns to education as the third example, we show how indices constructed from survey responses can be used to control for unobserved heterogeneity in individuals when good instruments are not available.
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