Thanks again.  This is exactly the answer that I was looking for.  ... View more

Larry and Steve, First of all, thanks so much for your responses.  I sincerely appreciate you both for taking the time to think about this problem and respond. A coworker of mine has the book that Larry referenced.  I'll take a look at it. While PROC GLM does always fit a fixed effect model, I don't believe that the same is true for PROC MIXED with the METHOD=TYPE3 option.  Here are several observations that make me believe that this is the case: The default ANOVA table created with PROC GLM is completely incorrect.  You need to specify the TEST option on the RANDOM statement to reproduce the tests created by PROC MIXED with the METHOD=TYPE3 option. With the G option on the RANDOM statement, PROC MIXED with METHOD=TYPE3 will print the estimated G covariance matrix.  If PROC MIXED fit a fixed effects model, then the G matrix does not exist. With the SOLUTION option on the RANDOM statement, PROC MIXED with METHOD=TYPE3 will produce EBLUPs for the observed levels of the random effects.  I don't think that it's possible to create EBLUPs with a fixed effects model. ESTIMATE and CONTRAST statements involving only fixed effects produce totally different results in PROC MIXED with METHOD=TYPE3 than in PROC GLM.  This is because PROC GLM does not correctly compute the standard errors. Also, I think that PROC MIXED with METHOD=TYPE3 does use the broad inference space while PROC GLM uses only the narrow inference space.  To see all this, compare the output produced by the following two steps.  Note that the "U.S. - Narrow Space" estimate in PROC MIXED with METHOD=TYPE3 is equivalent to the ESTIMATE statement produced by PROC GLM.  (Sorry if there are any typos in the code, I don't have SAS on this computer.) proc mixed data=sashelp.shoes method=type3;     where region in ('United States' 'Western Europe');     class region product;     model sales=region/ddfm=satterth;     random product region*product / solution g;     estimate "U.S. - Broad Space" intercept 1 region 1 0;     estimate "U.S. - Narrow Space" intercept 8                                                    region 8 0 |                                                    product 1 1 1 1 1 1 1 1                                                    region*product 1 1 1 1 1 1 1 1 /divisor=8; quit; proc glm data=sashelp.shoes;      where region in ('United States' 'Western Europe');      class region product;      model sales = region product region*product;      random product region*produce/test;      estimate "U.S. with GLM" intercept 1 region 1 0; quit; Based on these results, I'm inclined to believe that the tests created with PROC MIXED and METHOD=TYPE3 are for valid mixed effect models.  Am I still missing something here? I don't argue with any of the virtues of using REML over the EMS method.  I used METHOD=TYPE3 in this particular application only because the report I was generating has an expected format that includes an ANOVA table.  Whether or not this format is appropriate is certainly debatable, but that was not my call.  In fact, my question has nothing to do with REML at all.  I'm not trying to compare one test generated with REML estimates of the VCs to another test that uses EMS estimates of the VCs.  I'm only using the EMS approach via the METHOD=TYPE3 option.  My question is about the two tests of the same hypothesis that are both generated with the METHOD=TYPE3 option. Thanks again.  ... View more

Steve, I probably could have chosen my words better.  I agree that it's not appropriate to pick a test after running the test, so there's no need to open up a can of Bayesian stats on me right now   With the METHOD=TYPE3 option, SAS produces two different tests of the same hypothesis that can have different results when the design is unbalanced.  I just want to understand, on a high level, what the difference is between the two tests.  If one test is not valid or one test is preferable to the other, then I want to know that. It is a very basic two-way crossed unbalanced design with one fixed factor and one random factor.  Here is a silly example that is somewhat analogous: proc mixed data=sashelp.shoes method=type3;      where region in ('United States" "Western Europe");      class region product;      model sales = region/ddfm=satterth;      random product region*product; quit; Thanks again; ... View more

Hi.  Thanks for your response.  However, I still don't completely understand. The main reason for using the METHOD=TYPE3 option instead of REML is the ANOVA table in the output.  Some folks still want to see the sum of square breakdown.  Call them old-fashioned I guess.  The ANOVA table contains tests for both fixed and random effects.   My question relates to how the tests for fixed effects in this table relate to the "Type 3 Tests for Fixed Effects." You said that "The tests displayed in the table, "Type 3 Test for Fixed Effects", refer to tests of the fixed effects and are unrelated to the tests above of the variance components."  Maybe I am misunderstanding something, but I don't believe that this statement is accurate.  I'm pretty sure that the estimated V covariance matrix, based on the method-of-moments estimators, are used to construct the test statistic.  Therefore you would not get the same results of these tests if you used a different method of estimating the covariance parameters.  I specified the DDFM=SATTERTH option because I believe that PROC GLM (or PROC MIXED with the METHOD=TYPE3 option) uses the Satterthwaite approximation whenever the error term for one factor in the model does not equal the expected mean square value of another factor.  I was hoping that this option would make the two test equivalent, but no dice. From what I can tell, the test in the ANOVA table and the "Type 3 Test for Fixed Effects" are always the same when the design is balanced, but I'm not positive.  I know that the tests in the ANOVA table are not exact when you have unbalanced data.  Does anyone know if the other test is an exact test?  Also, I can recreate the "Type 3 Test for Fixed Effects" using a CONTRAST statement, but not the ANOVA test.  I tried to look through the SAS documentation on the fixed effects test, but I only found a mess of complicated matrix equations.  It's been about seven years since I've last opened my linear models textbook, and I'm hoping that I won't need to now as I'm more than a bit rusty. I have a situation where the p-value is slightly less than the significance level on one test and slightly more than the significance level on the other test.  If possible, I would like to justify using one test or the other. Thanks again, Jeremy ... View more

Thanks so much.  This has been a big help.  Your RANDOM statement did speed processing considerably.  I also added the TYPE=FA0(2) option to the RANDOM statement because I came across an example that recommended this covariance structure (or TYPE=UN) for random coefficient models. ... View more

Thanks so much for your helpful response.  You said that the syntax is for SAS/STAT 12.1.  Unfortunately, I'm still stuck in SAS 9.1.  The levels of factor2 are not the same for every level of factor1, so the design is nested. I thought about the problem some more today and came up with the following PROC MIXED step that I think does the trick.  Using this model, there is both a fixed and a random component to the slopes and intercepts.  However, I've never seen a model quite like this and I'm operating a bit outside of my comfort zone.  Does what I'm doing make sense? proc mixed data=mydata;      class factor1 factor2;      model response=factor1 covariate*factor1/noint solution;      random factor2(factor1) covariate*factor2(factor1)/solution;      estimate "Intercepts: Level A - Level B" factor1 1 -1;      estimate "Slopes: Level A - Level B" covariate*factor1 1 -1; quit; Thanks again. ... View more