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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.

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If you're getting a high reject rate it implies your proposal distribution is too wide.

Are you getting fuzzy caterpillar plots (WinBugs makes these)? They are a good diagnostic of model behavior.

MCMC models don't converge in the usual sense. Rather they continually sample from the uncertainty distribution, and those samples give you estimates of mean and variance-covariance of parameters.

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  • $\begingroup$ Ok. Thank you for the input. I will go back and try with a less wide proposal distribution. I'm still in the process of relearning the basics of MCMC. I will have to learn how to make caterpillar plots in R to do so. Right and the estimates are just nonsensical (all zero's etc). The poor convergence appears as I add more sample to the data as the parameters "converge" asymptotically to their values. $\endgroup$ – stat-o-matic Jul 1 '13 at 17:33
  • $\begingroup$ @stat-o-matic: This is the book I found most helpful. $\endgroup$ – Mike Dunlavey Jul 1 '13 at 18:15

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