The BGLIMM Procedure

In GLMMs, flat priors on the fixed-effects coefficients () are considered to be noninformative. The flat prior assigns equal likelihood for all possible values of the parameter, . This is the default prior for the fixed-effects coefficients in PROC BGLIMM.

In addition to the flat prior, a normal prior that has very large variance is also considered to be noninformative or weakly informative. The following statement specifies such a prior:

model y = x / cprior=normal(var=1e4);

This normal prior is noninformative because its variance value is sufficiently larger than the posterior variances of all the parameters.

On the other hand, you can use an informative prior by making the variance small in the normal distribution. If you want to have a specific mean and covariance for the normal prior, you can provide a SAS data set that contains the mean and covariance information of the normal prior through the INPUT=SAS-data-set in the CPRIOR= option,

model y = x / cprior=normal(input=MyPrior);

where MyPrior is the name of a SAS data set.