Decimals in Degrees of freedom, proc mixed

[satish123]

Hi all,

i ran proc mixed today, and got this

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	F Value	Pr > F
TRT	1	51.1	8.64	0.0049

Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > |t|	Alpha	Lower	Upper
T Vs R	-3.3302	1.1331	51.1	-2.94	0.0049	0.1	-5.2285	-1.4320

is it obvious that DF comes in decimals? can you guys explain?

code:  PROC MIXED Data=pk_data;
           CLASSES Sub Trt;
           MODEL data= Trt/ DDFM=SAT;
           RANDOM Trt/TYPE=FA0(2) SUB=Sub G;
           REPEATED/Group=Trt Sub=Sub;
           ESTIMATE 'T Vs R' trt -1 1/CL ALPHA=0.1;
           ODS OUTPUT G=Gmatrix;
           ODS OUTPUT ESTIMATES=EST;
           Run;

info: Total Subjects:52, Treatments:2, DF_method: Satterthwaite.

SAS version: SAS 9.4 Enterprise guide

Thanks,

Satish.

[lvm · Accepted solution]

In the world of mixed models, one has to drop old pre-mixed-model concepts, such as integer degrees of freedom.  You are using the Satterthwaite df calcuation method, which is an estimation based on the estimated variance-covariance G and R matrices. (G for random effects, R for repeated measures). Actually, I recommend the ddfm=KR with any repeated measure. 

The idea is this: to test a null hypothesis, F (or t) statistic should have an F (or t) statistical distribution when the null hypothesis is true. With mixed models (with random effects, correlations, ...), F (or t) statistic is only approximately distributed as F (or t) under H0; the approximation is best when the denominator df are calculated based on the model and the estimated G and R. Another way to look at this: The traditional df calculation methods do not account for the fact that the variances and covariances are estimated. The  KR method does take the uncertainty of the variance-covariance estimates into account in the df calcuation. Moreover, the KR method also adjusts the SEs of the fixed effect estimates based on the uncertainty of the variance-covariance estimates.