Just a short follow up. Be warned that hypothesis testing for the GLM (or other) parameterization is a huge topic, and there are many issues. With the GLM parameterization, the type 3 tests for main effects are tests of marginal means (means averaged over the levels of the other factors). SAS has detailed discussions in the GLM PROC chapter and in a general chapter on type 1- 4 hypothesis tests. For the other parameterizations, the documentation is less extensive. The chapter for SURVEYLOGISTIC has some useful text: For full-rank parameterization (such as reference, effect, and about everything except GLM), "The Type 3 test of an effect of interest is the joint test that the parameters associated with that effect are zero.". This is what we discussed already. So all is clear. But then it expands on this, "For a model that uses reference parameterization (as specified by the PARAM=REF option in the CLASS statement), the Type 3 test is [also] a test of the equality of cell means at the reference level of the other model effects". I had to think about this for a while, but I see this now for simple situations. Note that these are the cell means, not the marginal means, This is important. A test of A is for the equality of the A cell means at the chosen reference level of B. I would call these slices of interaction means (or simple effects); these are GLM-based terms. But the parameters don't allow you to test the equality of cell means of A at the non-reference level (I don't think these can be defined). The presence of an interaction makes this even harder to interpret. I think all is fine if you stick with the simpler interpretation of a "joint test that the parameters associated with the effect are zero". Use GLM parameterization if you want straight-forward interpretation of main effects and interactions.
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