The PROC MIXED documentation below has detailed information on how n and d are determined for various situations --
https://go.documentation.sas.com/doc/en/pgmsascdc/v_014/statug/statug_mixed_syntax01.htm#statug.mixed.procstmt_ic
So, n equals the number of effective subjects as displayed in the "Dimensions" table, unless this value equals 1, in which case n equals the number of levels of the first random effect you specify in a RANDOM statement. In your case, n=4 for BIC.
For restricted likelihood estimation, d equals q, the effective number of estimated covariance parameters. In your case, d=11 for the UN model and d=2 for the VC model.
The BIC value for model 1 = -2l + d*logn = 17.0 + 11*log(4) = 32.2
The BIC value for model 2 = -2l + d*logn = 27.1 + 2*log(4) = 29.9
They are consistent with PROC MIXED output.
As far as "inconsistency" between AICC and BIC -- I do not compare these two fit statistics among themselves. I compare the same fit statistics (AICC or BIC) across different models. And I assume that is what these fit statistics are used.
I am not sure what other sources you read about BIC. I am personally not aware of a reference where n and d are defined explicitly for models with RANDOM and REPEATED statements for all these fit statistics. But it could just be my ignorance. Our developers did their research and came up with these calculations for various data and modeling situations. If you have good references for different computations please share it with me, I would appreciate that.
Thanks,
Jill
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