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# Decimals in Degrees of freedom, proc mixed

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 StandardError 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.

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Solution
‎08-29-2016 11:02 PM
Valued Guide
Posts: 684

## Re: Decimals in Degrees of freedom, proc mixed

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.

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Solution
‎08-29-2016 11:02 PM
Valued Guide
Posts: 684

## Re: Decimals in Degrees of freedom, proc mixed

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.

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