Why Do I Get Different Results of Variance Component analysis Between SAS and JMP ??

[#1]

Why Do I Get Different Results between SAS and JMP for Variance Component analysis?

Case 1 - Crossed then Crossed 

proc varcomp data = data method=TYPE1;
class Factor1 Factor2 Factor3;
model variable = Factor1 Factor2 Factor3;
run;
= JMP - Quality and Process - Variability / Attribute Gauge Chart - Model Type - Crossed 

(If "Main Effect" is selected, the result is the same with SAS.)

Case 2 - Nested then Crossed 

proc varcomp data = data method=TYPE1;
class Factor1 Factor2 Factor3;
model variable = Factor1 Factor2(Factor1) Factor3;
run;
= JMP - Quality and Process - Variability / Attribute Gauge Chart - Model Type - Nested then Crossed

Case 3 - Crossed then Nested 
proc varcomp data = data method=TYPE1;
class Factor1 Factor2 Factor3;
model variable = Factor1 Factor2 Factor3(Factor2);
run;
= JMP - Quality and Process - Variability / Attribute Gauge Chart - Model Type - Crossed then Nested

It was confirmed that the SAS and JMP results of Variance Component are the same when the number of factors is 1 or 2.

However, the results are different for the above cases with 3 factors.\

I would really appreciate it ...if you could tell me why the results of the two programs are different !

[#2]

Without seeing your data I can't be sure of why they are different, but I can make an educated guess.

In the SAS code you are using Method=Type I. This is using a type I sums of squares for the estimation. In the JMP Variance Components dialog, there is a button for Analysis Settings. If you click that you will see that JMP's default is to "Choose best analysis". So JMP could freely switch between EMS, REML, or Bayesian. So JMP is likely using a different estimation method than SAS. Note that JMP does not even provide an option to force the Type I (or EMS) method since that is an older approach that is not generally recommended.

If you need them to agree, in SAS set the method to REML. In JMP, choose the Use REML analysis. That should make them agree. But keep in mind that even in this situation, depending on your data, there may be slight differences due to the approach of how large matrices may be handled (split apart and recombined) for efficiency purposes as well as the iterative nature in solving such equations.

[#3]

Dear Dan,

Thank you so much for your kind reply.
As you said, I've got the same results when using REML.

I understood that the same result cannot be obtained in the case of non-REML because the estimation method of the type1 error method and the EMS method are different.

You said that the Type1 method is an old method.

Can using REML get more accurate ANOVA results even if variacne is not negative???

[#4 · Accepted solution]

What exactly is meant by accurate? The Type I or EMS approach and REML are just different estimation methods. REML is a very good and well-respected estimation method that has been around for years. In fact, for most situations with balanced data, it will provide the same results as EMS. REML has the advantage of working in unbalanced situations and in situations with negative variance components. Further, REML would even allow you to REQUIRE the variance components to be greater than or equal to zero to avoid the negative estimates.

You can feel comfortable with the REML approach.

[#5]

Thanks for your really kind and specific reply !!