PROC GENMOD BAYES - Variance vs. Covariance for prior input dataset produces different answers. Why?

[evardoodle]

Hello SAS Experts,

When using PROC GENMOD for a Bayes analysis, I noticed there is a substantial difference in my posterior estimates when entering in the exact same prior regression information using the coefficient means and full covariance matrix vs. the coefficient means and just the coeffient variances. I set a seed for reproducilibity and both models appear to achieve convergence. Please review my code, input priors, and results below.

Here is my code:

  proc genmod data=data;
  model DGSYTOT1 = totpcbla RIDAGEYR totpcbla_RIDAGEYR RIAGENDR smoker HSplus / dist=normal link=identity;
  bayes coeffprior=normal(input=prior)  seed=12345
  plots=all stats(percent=2.5 50 97.5) diagnostics=all outpost=post;
  run;

Here are the prior datasets with theoretically equivalent information:

Here are the disparate results:

I would report very different interpretations of these results and I am not sure which results to trust. Can anyone explain why the input dataset structure matters so much? Is this an estimation error? Am I inputting something incorrectly?

Any help would be greatly appreciated. Thanks in advance!

Eva

[evardoodle]

A very helpful person helped me solve this problem. When you only input prior variances, SAS assumes all covariances are 0, it does not compute the actual covairances. I confirmed this by setting covariances to 0 in the covariance matrix and obtained the same results as inputing variances only.