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Publication date: 11/10/2021

The Kackar-Harville Correction

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. The rationale for this approach is that corrections for BLUPs can be computationally and memory intensive when the random effects have many levels.

In SAS, the Kackar-Harville correction is done for both fixed effects and BLUPs only when the DDFM=KENWARDROGER is set.

Standard errors for linear combinations involving only fixed effects parameters match PROC MIXED DDFM=KENWARDROGER. This case assumes 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 match PROC MIXED DDFM=SATTERTHWAITE.

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=SATTERTHWAITE and DDFM=KENWARDROGER options. If the data are balanced, JMP matches SAS for balanced data, regardless of the DDFM option, because the Kackar-Harville correction is null.

Degrees of Freedom

The degrees of freedom for tests involving only linear combinations of fixed effect parameters are calculated using the Kenward and Roger correction. Therefore, the JMP results for these tests match PROC MIXED using the DDFM=KENWARDROGER option. If there are BLUPs in the linear combination, JMP uses a Satterthwaite approximation to get the degrees of freedom. The results then follow a pattern similar to what is described for standard errors in the preceding paragraph.

For more information about the Kackar-Harville correction and the Kenward-Roger DF approach, see Kenward and Roger (1997). The Satterthwaite method is described in detail in the MIXED Procedure chapter in SAS Institute Inc. (2020d, ch. 83).

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