In short, I need to decompose the fitted values obtained from ANOVA into components corresponding to each term in ANOVA statement. This problem appears trivial, but it becomes tricky when GLM coding is used for the design matrix. Let's take a balanced 2*2 ANOVA with 2 observations per cell.   Y = A + B + A*B GLM coding produces 8*9 design matrix: Intercept – column 0 Main effect of A – columns 1-2 Main effect of B – columns 3-4 Interaction – columns 5-8   The estimated coefficients, b, look like (4 estimable parameters, as expected): b0 b1 b2 b3 b4 b5 b6 b7 b8 5.5 -0.915 0 1.15 0 -0.36 0 0 0   Let's take the covariate pattern: 1 1 0 1 0 1 0 0 0 for which the fitted value is 5.375. One could say that it's decomposed as   5.375 = 5.5 (Int) - 0.915 (A main effect) + 1.15 (B main effect) - 0.36 (A*B interaction)   but that's not the case. The linear restrictions for Type III hypotheses to test the significance of the two main effects and interactions are created as specified here.  In particular, to test   H0: Main effect of A = 0,   we test whether k′b where k is (defined up to a multiple):   0 0.894427 -0.894427 0 0 0.447214 0.447214 -0.447214 -0.447214   That shows that, for the given covariate pattern, the point estimate of A main effect depends on both b1 and b5, not just b1. To test H0: Main effect of B = 0, we use the restriction:   0 0 0 0.894427 -0.894427 0.447214 -0.447214 0.447214 -0.447214   and for H0: A*B = 0 it is:   0 0 0 0 0 1 -1 -1 1   These linear restrictions are called "Type III estimable functions" in PROC GLM and "Type III coefficients" in PROC MIXED. The problem is I don't know how to use all that information in order to obtain the point estimates of main effects and interactions for a given covariate pattern. ... View more

  Hello:   I am running a macro with a large number of Negative Binomial regressions in GENMOD. I know that in some cases the result is questionable (due to a negative overdispersion parameter) but still GENMOD outputs non-missing results from ESTIMATE in all cases, including the models that produce warnings like:   WARNING: The relative Hessian convergence criterion of 0.01955056 is greater than the limit of 0.0001. The convergence is questionable. WARNING: The procedure is continuing but the validity of the model fit is questionable.   Is there a way to tell GENMOD to output nothing or missing values when the model fit generates warnings? ... View more

Hello: Please help me sort out this output of Negative Binomial regression in PROC GENMOD. The model includes a binary factor, Factor_B. There are a few p-values associated with Factor_B that I expect to be consistent (see the attachment): 1) In “Analysis of Maximum Likelihood estimates” Wald p-value for the corresponding regression coefficient (0.0226) 2) LR test, Type 3, (0.8667) 3) Wald test, Type 3, (0.8666) 4) Contrast “B1 vs B2”, LR (0.8667) 5) Contrast “B1 vs B2”, Wald (0.8666) As you can see, 1) seems to be a problem. Why is it so different? Note also that the problem showed up only after I fitted the model with Factor_A*Factor_B interaction. In the additive version, everything was consistent. ... View more