Selection of random coefficients in ordered response models: a framework to detect heterogeneity in household surveys

This paper develops a Bayesian method to detect heterogeneity in the relationship between covariates and the outcome in models with ordered responses. To this end, we construct an efficient Markov chain Monte Carlo algorithm for a hierarchical Bayesian model that selects random coefficients in ordered models. This method extends an approach for selecting random coefficients in linear mixed models into the ordered setting by adding two enhancements that are relevant to the latter category of models. First, we construct steps to efficiently estimate cut-points by addressing identification and ordering constraints. Second, we develop a framework to evaluate marginal effects that combine the fixed and random effects of each covariate. The marginal effects additionally allow for model uncertainty by averaging across models visited by the selection algorithm. Simulation studies demonstrate that this method detects random effects when they are present, estimates parameters accurately and efficiently samples from the posterior with low autocorrelations across successive draws. On applying this method on data from the survey of consumer expectations, we find clear support for the presence of household-level heterogeneity in relationships between demographic variables, and current as well as expected financial conditions.