Bayesian Inference for a 1-Factor Copula Model

We develop efficient Bayesian inference for the 1-factor copula model with two significant contributions over classical inference. First, our approach leads to straightforward inference on the latent factor since iterates of the latent factor are generated as a by-product in the proposed Markov chain Monte Carlo algorithm. In contrast, there is no known classical approach for inference on the latents. Second, by developing a reversible jump Markov chain Monte Carlo scheme, we are able to select or average over factor copula specifications that are constructed from a large set of candidate parametric bivariate copula building blocks. Our approach can accommodate margins that are discrete, continuous or a combination of both. Through extensive simulations multiple schemes are compared on the basis of computational and Monte Carlo efficiency. The preferred schemes provide reliable inference on all parameters including the latent factor and model space. The potential of the proposed methodology is highlighted in an empirical study of ten binary variables measuring the multidimensional nature of poverty collected for 11463 East Timorese households. We construct a poverty index using estimates of the latent factor. Compared to a classical analysis, our method yields better out-of-sample fit and uncovers a variety of flexible relationships between the latent measure and observed variables by averaging over a diverse set of copulas.