08-23-2016 09:03 AM
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 | 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.
08-23-2016 04:44 PM
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.
08-23-2016 04:44 PM
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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