Modeling and Multivariate Methods - SAS

Appendix A Statistical Details 687
Details of Random Effects
Details of Random Effects
The variance matrix of the fixed effects is always modified to include a Kackar-Harville correction. The
variance matrix of the BLUPs and the covariances between the BLUPs and the fixed effects are not
Kackar-Harville corrected because the corrections for these can be quite computationally intensive and use
lots of memory when there are lots of levels of the random effects. In SAS, the Kackar-Harville correction is
done for both fixed effects and BLUPs only when the DDFM=KR is set, so the standard errors from PROC
MIXED with this option will differ from all the other options.
This implies:
• Standard errors for linear combinations involving only fixed effects parameters will match PROC MIXED
DDFM=KR, assuming that one has taken care to transform between the different parameterizations used
by PROC MIXED and JMP.
• Standard errors for linear combinations involving only BLUP parameters will match PROC MIXED
DDFM=SATTERTH.
• Standard errors for linear combinations involving both fixed effects and BLUPS do not match PROC
MIXED for any DDFM option if the data are unbalanced. However, these standard errors are between what
you get with the DDFM=SATTERTH and DDFM=KR options. If the data are balanced, JMP matches SAS for
balanced data, regardless of the DDFM option, since the Kackar-Harville correction is null.
The degrees of freedom for tests involving only linear combinations of fixed effects parameters are calculated
using the Kenward and Roger correction, so JMP's results for these tests match PROC MIXED using the
DDFM=KR option. If there are BLUPs in the linear combination, JMP uses a Satterthwaite approximation to
get the degrees of freedom. So, the results follow a pattern similar to what is described for standard errors in
the preceding paragraph.
For more details of the Kackar-Harville correction and the Kenward-Roger DF approach, see Kenward and
Roger(1997). The Satterthwaite method is described in detail in the SAS PROC MIXED documentation.