Bayesian Analysis of the Stochastic Switching Regression Model Using Markov Chain Monte Carlo Methods

In the stochastic switching regression model, it is not known which of several alternative regression models has actually generated the observed dependent variable. This study develops Bayesian methods for estimating the parameters of this model. A difficulty with this approach in this context arises because the direct evaluation of the posterior mean is complicated and cumbersome. An alternative to direct evaluation is the use of Markov Chain Monte Carlo methods. The particular methods examined here are data augmentation and Gibbs sampling, both of which use samples that are drawn from conditional distributions that are easier to derive and more feasible to sample from than the complex joint posterior distribution. The conditional distributions necessary to implement data augmentation and Gibbs sampling are derived in this study. A simulation study compares model estimates obtained using data augmentation, Gibbs sampling, and the maximum-likelihood EM algorithm. Two models are examined, a market-disequilibrium and a structural-change model. In the simulation study, special attention is given to the accuracy and bias of the researcher's prior distributions. The results suggest that data augmentation and Gibbs sampling perform similarly for all cases. When there is little or no bias in the mean of the prior distribution, the Bayesian estimates perform better than maximum-likelihood as long as the standard deviations of the regression coefficients are less than 1.0. When the standard deviations of the regression coefficients are between 1.0 and 2.0, the Bayesian and maximum-likelihood estimates are similar. With moderate bias in the prior mean, the Bayesian and maximum-likelihood estimates perform similarly. Large bias allows the maximum-likelihood method to perform better than the Bayesian estimator as long as the standard deviations of the regression coefficients are small.