Xiaoyu Qian writes:

I have a question when I apply the half-Cauchy prior (Gelman, 2006) for the variance parameter in a hierarchical model. The model I used is a three level IRT model equivalent to a Rasch model. The variance parameter I try to estimate is at the third level. The group size ranges from 15 to 44. The data is TIMSS 2007 data.

I used the syntax provided by the paper and found that the convergence of the standard deviation term is good (sigma.theta), however, the convergence for the parameter “xi” is not very good. Does it mean the whole model has not converged? Do you have any suggestion for this situation.

I also used the uniform prior and correlate the result with the half-Cauchy result for the standard deviation term. The results correlated .99.

My reply: It’s not a problem if xi does not converge well. It’s |xi|*sigma that is relevant. And, if the number of groups is large, the prior probably won’t matter so much, which would explain your 99% correlation.