The problem: SAS PROC MIXED Doc provides an example illustrating analysis of a Split-Plot experiment in a RCBD. There are two error terms for testing the factor effects: the whole-plot and sub-plot error. What is bizarre is that the ORDER of how these terms appear in the random statement effect the denominator Degrees of freedom for the "TYPE 3 Test of Fixed Effects". The models are exactly the same, produce the exact same variance components and -2LL value. EXACTLY THE SAME!!!

However, the ORDER on the RANDOM statement will yield different Denominator Degrees of freedom. What may be even more bizarre (with the rearranged random terms) is that if you specify "method=type3" the ANOVA table is correct, but the correct results are not being carried over to the "Type 3 Tests of Fixed Effects".

The problem is alleviated, by specifying DDFM=Satterth or using a "repeated" statement. However, can someone kindly explain to me how two models, that are exactly the same, yield different statistics? Is this something internal with PROC MIXED?

This whole thing came about b/c I am analyzing a similar experiment, accept mine is replicated across multiple locations and I notice this same phenomenon. However, in my experiment, the locations and whole-plot factor are random. So there are a lot of terms to specify on the "random" statement. I just hate to think that the "order" of these terms could effect the results...Even though I could use (and am) a DDFM adjustment, I want to know what is going on.

Any thoughts/comments? Below is the code and examples.

Thanks, Lewis

/* http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_mixed_sect030.htm */

/*This example comes directly from the PROC MIXED documentation. The experiement was a split-plot in a RCBD. There are 3-levels of the whole-plot factor A, and 2-levels of the sub-plot factor B. A total of 4-blocks were used. For a split-plot in a RCBD, the Numerator and Denominator Degrees of freedom for testing the whole-plot and sub-plot factors are:

Factor Num DF Denom DF A (whole-plot) (A-1)=2 (A-1)(Block-1)=6 B (Sub-plot) (B-1)=2 A(B-1)(Block-1)=9 A*B (A-1)(B-1)=2 A(B-1)(Block-1)=9

*/

data sp; input Block A B Y @@; datalines; 1 1 1 56 1 1 2 41 1 2 1 50 1 2 2 36 1 3 1 39 1 3 2 35 2 1 1 30 2 1 2 25 2 2 1 36 2 2 2 28 2 3 1 33 2 3 2 30 3 1 1 32 3 1 2 24 3 2 1 31 3 2 2 27 3 3 1 15 3 3 2 19 4 1 1 30 4 1 2 25 4 2 1 35 4 2 2 30 4 3 1 17 4 3 2 18 ; proc print; run;

*(1) Correct; *Split-Plot in RCBD (Sas online doc model); proc mixed data=sp lognote; class A B Block; model Y = A B A*B; random Block A*Block; run;

*(2) Incorrect: *Rearranged random terms!! TYPE III Tests for Whole-plot factor A are WRONG; proc mixed data=sp lognote; class A B Block; model Y = A B A*B; random A*Block Block; run;

*(3) Partially Correct: *Rearrange random terms look at ANOVA TABLE. Correct error term,Den DF & p-value being used for A: MS(A*BLOCK),but wrong DF reported in 'Type 3 Tests of Fixed Effects'; proc mixed data=sp method=type3 lognote; class A B Block; model Y = A B A*B; random A*Block Block; run;

*(4) Correct: rearrange random terms and use SATTERTHWAITES DF; proc mixed data=sp lognote; class A B Block; model Y = A B A*B/ddfm=satterth; random A*Block Block; run;

*(5) Correct: *Use repeated statement for A*Block and use SATTERTHWAITES DF; proc mixed data=sp lognote; class A B Block; model Y = A B A*B/ddfm=satterth; random Block; repeated/subject=A*Block type=cs rcorr r; run;

***************************** Lewis Jordan Weyerhaeuser: Southern Timberlands R&D Cell (Primary): 662-889-4514 Office: 662-245-5227 lewis.jordan@weyerhaeuser.com<mailto:lewis.jordan@weyerhaeuser.com> *****************************