Bayesian Inference for the One-Factor Copula Model

ABSTRACT

We develop efficient Bayesian inference for the one-factor copula model with two significant contributions over existing methodologies. First, our approach leads to straightforward inference on dependence parameters and the latent factor; only inference on the former is available under frequentist alternatives. Second, we develop a reversible jump Markov chain Monte Carlo algorithm that averages over models constructed from different bivariate copula building blocks. Our approach accommodates any combination of discrete and continuous margins. Through extensive simulations, we compare the computational and Monte Carlo efficiency of alternative proposed sampling schemes. The preferred algorithm provides reliable inference on parameters, the latent factor, and model space. The potential of the methodology is highlighted in an empirical study of 10 binary measures of socio-economic deprivation collected for 11,463 East Timorese households. The importance of conducting inference on the latent factor is motivated by constructing a poverty index using estimates of the factor. Compared to a linear Gaussian factor model, our model average improves out-of-sample fit. The relationships between the poverty index and observed variables uncovered by our approach are diverse and allow for a richer and more precise understanding of the dependence between overall deprivation and individual measures of well-being.

KEYWORDS:

• Model selection
• Multidimensional poverty index
• Multivariate analysis
• Reversible jump MCMC
• Vine copulas

Acknowledgments

The authors thank associate professor Xibin Zhang from Department of Econometrics and Business Statistics, Monash University, Australia for bringing our attention to the adaptive method using Robbins-Monro process proposed by Garthwaite, Fan, and Sisson (2016) which significantly improves the efficiency of their sampling algorithm. The authors thank Professor Brett Inder from Department of Econometrics and Business Statistics, Monash University, Australia for providing them with the dataset for East Timor. The authors also thank Professor Mervyn Silvapulle, for providing general comments and feedback. All analyses in this study were conducted using R Studio Version 1.0.153 with the aid of R packages such as mcmc, coda, CDVine, copula, vine, ggplot2, and maptools. R code is also provided.