Programming the statistical procedures from SAS

Decimals in Degrees of freedom, proc mixed

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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

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.

 


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