Why? PROC GLIMMIX parameterizes both the G-side and the R-side using the same statement, RANDOM, with the exception that the R-side requires either the keyword, _RESIDUAL_, or the option, RESIDUAL. Of the distributions that PROC GLIMMIX can estimate, the normal distribution, the lognormal distribution, and the t-distribution have "separable" errors as you have defined them, where the mean and the variance are NOT functionally related; in all other distributions, the variance depends on the mean. Since you can have either a G-side matrix, an R-side matrix, or both, it is unclear to me why you would want to restrict some of the distributions to one "side" and others to the other "side". The variance of the observations, given the random effects, equals A**(0.5)*R*Tr(A)**(0.5), where A is a diagonal matrix of the variances of the different distributions. For the distributions with "separable" errors, A is the identity matrix. By default, the R matrix is the scaled identity matrix, which for distributions with "separable" errors has a scale value = 1.00. So, unless you specify a different variance-covariance structure for this R-side matrix, the distributions with "separable" errors (except for the t-distribution) will have variances that are the identity matrix.
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