Using Stan for Spatial Smoothing of Regression Parameters
We have developed a Stan program that will do spatial smoothing of regression parameters. In the hierarchical model, the coefficients vary at every location, but are correlated across space. Our model smooths all parameters with their own smoothing parameters. We have not found any comparable model in previous literature, although there is bound to be one somewhere. The application is for U.S. crop yields and a time trend model. In the model, different intercepts, time trends and variances are estimated for every county. The Bayesian estimation allows more precise estimates by using values of nearby counties as part of the estimation. It is like geographically weighted regression except that the weights are estimated rather than assumed. We are very happy with the estimates that we are getting from Stan and the model does converge. Stan is faster than our previous MCMC program and the MCMC did not converge anyway. But, the program can still take days to run when the number of locations is in the hundreds. We are interested in ideas about how to speed up our calculations. The talk is also an opportunity to summarize what we see as the strengths and weaknesses of Stan.
The MCMC version of the paper is available at https://ageconsearch.umn.edu/record/274403?ln=en
B. Wade Brorsen is regents professor and A.J. and Susan Jacques Chair in the Department of Agricultural Economics at Oklahoma State University. He is a fellow of the Agricultural and Applied Economics Association and a former editor of American Journal of Agricultural Economics. He has published well over 200 refereed journal articles. He is an applied econometrician who uses Bayesian methods when needed. His interest in Bayesian methods includes spatial smoothing as well as estimating systems of equations. While most of his education is in agricultural economics, he also has a MS in Statistics from the University of Wisconsin.