This issue is not related to why you are finding differences between GLIMMIX and LOGISTIC output. That is still unresolved. My explanation primarily involved non-centered x variables. But with generalized linear models (GLM), or generalized linear mixed models (GLMM), things are more complicated. The logit intercept (link of the expected value ) depends on what x variables are in the model, even mean-centered ones.You are not necessarily getting an estimate that directly corresponds to the arithmetic average rate. ... View more

Several things to think about. First of all, you can directly compare LOGISTIC and GLIMMIX. Just take out the random statement from GLIMMIX and run. You should get the same results for the two procedures (intercept and coefficients). Second, in your reply to Steve, you said you thought you used quadrature, but your code does not show this. With random effects and binary data, it is critical that you use quadrature (method=quad), because the default RSPL (linearization) method can be very biased in this circumstance. The bias diminishes rapidly for binomial data as the number of trials per experimental unit goes up (but your data at 0:1, a trial size of 1). There can still be bias with quadrature, but much less so. Often, it is impossible to use quadrature because of memory/time constraints, as described in the user's guide, but try it as your first choice. If quadrature is not allowed, then use method=laplace. (These options won't affect your results when you remove the random statement, since these apply to models with random effects). Third, your reply suggests that you have convergence problems  (you mentioned nonexistence of a convergence point??? Not sure what you mean). This can drastically affect your results. Are you getting convergence? What is the estimated variance (and its SE)? My thoughts about decreasing intercept were more related to the situation where the covariates are not centered. Think of two covariates, x1 and x2. If only x1 is in the model, then the interecept is the expected response when x1=0; but x2 could be anything. Crudely, you are getting the expected response when x2 is at its center ((it is more complex than this, based on correlations of the x's  and other things). The intercept would not represent the situation with x1=x2=0. Now, if you add x2, the intercept is the expected response when x1=x2=0 (with x3, x4, ... being anything). As you add x's, you are pulling the intercept towards a global x1=x2=x3=...=0 case. I think this could get more complicated with a mixture of positive and negative correlations in the X matrix. But this is all likely off the point of your problem. ... View more

The intercept has the same interpretation in GLIMMIX as in LOGISTIC. But I see that you did not use a      class Hospital_ID; statement. Your results for the random-intercept model will be incorrect if Hospital_ID is not sorted prior to running GLIMMIX. If sorted, the results would be fine, but it is safer to use a class statement. To me it makes sense that the intercept could be getting smaller as you add covariates. You should realize that the covariates likely have high correlations, and it is unlikely that the point where all covariates are simultaneously at their means will exist with your dataset. You will need to show actual output if you need more help. ... View more

My suggestion would only work if you have a limited number of levels of the variables. The fact that you wanted to do orthogonal polynomials suggested a relatively small number of levels (unique values) for the variables. This is the usual situation when someone would use orthpolys. For your situation, you should not use my idea, nor should you use contrasts to deal with the topic. There are some examples in Littell et al. (2006), SAS for Mixed Models, 2nd edition, that would help you (for continuous and categorical variables in the same model). I personally would not worry much about orthogonality, a luxury that you don't need (or maybe can't afford). Especially with millions of observations. Are you working with nonnormal response variable? If you can assume normality, then I highly recommend PROC PLS for dealing with the correlations of the variables. This is a great procedure, primarily intended for all continuous predictor variables.No matter what approach you take, you probably will want to first work on a sample of your full data set to get the bugs worked out. Then fit the model to the full data set. ... View more

The size of your data set is not relevant in the use of IML for the coefficients. You only use IML to get the values, as you did. Then you would put these into contrast or estimate statements in GENMOD. Note that in CONTRAST, the coefficients must add to 0, exactly (not just to two or three decimal places, or whatever). You would rescale first: multiply these long decimals by a big number and then put in a / divisor=  option to bring these back to what you want. But with GENMOD, you can get orthogonal polynomial parameterization directly within the procedure. Make sure the levels of your factors are numeric (not letters, names, etc.). Then use: class factor1 factor2 / effect=orthpoly; Check out the GENMOD documentation for different ways of specifying the CLASS coefficients. I haven't used this option myself (I have used other effect= options), so I don't recall what happens when you specify interactions. ... View more

If you have sas 9.4 (released this summer), you can run the new HPGENSELECT for model selection with exponential-family distributions.Thus, you can do logistic regression. The proc is designed for Big Data problems, but runs on any data set. It does not have the full functionality of GLMSELECT, but it may be fine for your needs. I have not tried it yet (I still can't use 9.4) ... View more

If you are putting in the right coefficients in the estimate statement, you should not have any problem at all with getting estimable values (for the 'means' model). I can't tell from your posts where the problem lies, but the advantage of the 'means' model is that you can get results. I am guessing you are putting in nonzeros for the wrong terms. ... View more