The paper that Reeza refers to shows you how to write contrasts and estimates in terms of LS-means, using the LSMESTIMATE statement. If you have a very complex contrast, then expressing the contrast in terms of LS-means should be much easier than expressing the contrast in terms of the parameter estimates.
The FAQ posted here shows quite a few examples of writing CONTRAST and ESTIMATE statements. These examples walk you through forming the individual pieces of the contrast, in terms of the model parameters, and then forming the complete contrast from those pieces.
The most common mistake made in writing ESTIMATE statements involving interaction terms is not involving the main effects. Many contrasts that difference two levels of an interaction will involve coefficients on the main effects as well.
A grad school trick for forming a contrast involving an interaction is to use a table. Suppose we have a two-level factor, A, and a three-level factor, B. We want to form the contrast between A1B1 and A2B2. Create a table that has the six cells for that 2x3 interaction and put a 1 in the cell for A1B1 and a -1 in the cell for A2B2:
B
1 2 3
1 1
A
2 -1
Then add across the rows and columns to get the marginal totals for the table:
B
1 2 3 Total
1 1 1
A
2 -1 -1
Total 1 -1
The entries in the body of the table give you the coefficients for the interaction term on the ESTIMATE statement. The marginal totals of the rows and columns give you the coefficients for the main effects. For this example, you would have
estimate 'A1B1 vs A2B2' a 1 -1 b 1 -1 0 a*b 1 0 0 0 -1 0 / e;
This parameterization assumes GLM coding and that the factor A is listed before the factor B on the CLASS statement.
Another way to build out your estimate statement is to do so in pieces. For the same example above (again assuming GLM coding), the estimate for A1B1 would involve the first level of A, the first level of B, and the A1B1 interaction level. That ESTIMATE statement would look like
estimate 'A1B1' int 1 a 1 0 b 1 0 a*b 1 0 0 0 0 0 / e;
Now do the same thing for A2B2:
estimate 'A2B2' int 1 a 0 1 b 0 1 a*b 0 0 0 0 1 0 / e;
If you want to create the estimate for the difference of those two interaction cells, then difference the elements of the two ESTIMATE statements. Put minus signs in front of the terms of the second ESTIMATE statement (the one for A2B2). Combine those with the terms from the first ESTIMATE statement. The terms for the intercept cancel, you should get A 1 -1 for the terms on A, B 1 -1 0 for the terms on B, and A*B 1 0 0 0 -1 0 for the terms on the interaction. Combine those on an ESTIMATE statement, and you duplicate the result we see from the table approach above.
You can follow this approach for any estimate you need. The details in that FAQ here should help with more complicated contrasts and estimates.
