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 .
Beliefs are important determinants of an individual's choices and economic outcomes, so understanding how they differ across individuals is of considerable interest. Researchers often rely on surveys that report individual expectations as qualitative data. We propose using a Bayesian hierarchical latent class model to summarize and interpret observed heterogeneity in categorical expectations data. 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 beliefs 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 .
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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
Beliefs are important determinants of an individual's choices and economic outcomes, so understanding how they differ across individuals is of considerable interest. Researchers often rely on surveys that report individual expectations as qualitative data. We propose
R
that is adapted from probabilistic topic modeling of text data
to summarize and interpret observed heterogeneity in categorical expectations data. We show that the statistical model corresponds to an economic structural model of information acquisition, which guides interpretation and estimation of the model parameters
A
beliefs follow a dynamic structure and
R
no longer available
not appropriate
R
classes
belief types
R
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
Two examples are considered. The first shows
A
the
R
Using returns to education as the third example, we show how indices
The second shows that belief types
R
to control for unobserved heterogeneity in individuals when good instruments are not available
in a subsequent analysis to estimate heterogeneous returns to education