The code and data I am borrowing come from http://www.perossi.org/home/bsm-1 under CS 5 from the book Bayesian Statitics and Marketing. I tried applying their model to another dataset and am getting failed convergence/terrible results. I am simply looking for conceptual reasons why I might be getting what I am seeing.
I am able to duplicate the results from the book using the code. I then took the code, modified it to run on my own set of data and get a failed convergence (almost perfect reject rate, log likelihood still decreasing, parameters stuck or widly moving across their support space).
Almost immediately, my beta_ij parameters (see model description below) get stuck at zero and never budge. When I only run the code on a subsample of records, I get reasonable results. There are a lot of zero quantities in the data where x_i's would be zero for many of the products.
The model is of the form:
Utility of product i and household j = beta_ij + delta_i log( x_i + 1), where beta_ij are drawn from a normal distribution, delta_i from a uniform (-1, 0) and x_i are the quantities purchased of product i.
The random effects model parameters are given priors, the mean, beta_bar is modeled as a multivariate normal and the variance-covariance matrix is modeled as an inverse-wishart.
The code draws first the prior parameters given the household beta_ij's, then draws for the delta_i's and finally updates the beta_ij's given these new parameters. For the book reference, these are formulas CS5.4 - CS5.7 on page 271 of Bayesian Statistics and Marketing by Rossi, Allenby and McCulloch.
Thank you and any thoughts would be appreciated.