Lots of ways of doing this with proc mixed and glimmix for hierarchical models. This old article is technically about repeated measures in GLM and MIXED, but is ultimately a comparison of MANOVA in the two procedures. https://support.sas.com/rnd/app/stat/papers/mixedglm.pdf Here is a more recent blog on the topic: http://blogs.sas.com/content/sastraining/2011/02/02/the-punchline-manova-or-a-mixed-model/ The syntax is different, and the data are stacked, for analysis in MIXED and GLIMMIX compared with GLM, but you can handle so many more situations with the mixed-model procedures. You are not even restricted to the same distribution. One of the nice examples in the User's Guide for GLIMMIX deals with a multivariate analysis of two random variables, one binary (Bernoulli) and the other count (Poisson). SAS/STAT(R) 9.3 User's Guide ... View more

Another general approach is to put the GENMOD results in an item store, and then use PROC PLM for post-model-fit processing. The ESTIMATE statement in PLM allows for an ILINK option. This way you don't need to use a dummy variable for the intercept. proc genmod data=x; model Success/Attempts = / link=logit dist=binomial type1 type3; store results; run; proc plm restore=results; estimate 'intercept' int 1 / ilink; run; ... View more

Different possibilities. What is your goal? Simultaneous modeling of all the (possibly correlated) response variables or just having a convenient way of getting separate analyses for several response variables? Check out PROC PLS (partial least squares). ... View more

A nice trick by Rick to get the inverse link. ... View more

Rick's approach works when one is using the log link. But the OP is using the logit link (which is the default and canonical link for the binomial). I am surprised that GENMOD does not have an ILINK option. I use is all the time with GLIMMIX. ... View more

You are getting the intercept on the logit link scale. The inverse link is 1/(1+exp(-(-0.1761))) = .456, the required answer. I can get this directly by using GLIMMIX instead of GENMOD, with the ILINK option on an ESTIMATE statement. proc glimmix data=x; model Success/Attempts = / link=logit dist=binomial s ; estimate 'intercept' int 1 / ilink ; run; This gives you the logit link intercept (-.1761), and the inverse link (labeled mean; .456). However, the ILINK option is not valid in GENMOD. I don't use GENMOD a lot, but I am not aware of an easy way to get the inverse link with this procedure. ... View more

You can definitely do noninferiority power calculations. Here is a good description for some of this. Check the User's Guide for other applications. 48616 - Design and analysis of noninferiority studies ... View more

Here is a good place to get started: http://support.sas.com/documentation/onlinedoc/stat/930/introreg.pdf ... View more

I also question your need for different variances for each treatment. Did you look at this to see if it is justified? You can compare models with and without the group effect for the random term by comparing log likelihoods, but only if you use method=laplace. ... View more

You can do the same thing with a random _residual_; term in your model. But I recommend against it. By doing so, you are entering the realm of quasi-likelihood, where the "distribution" is no longer what you think it is (there is no discrete distribution that has the form you get with "Poisson" and over- or under-dispersion). When possible, deal with a real distribution. Your underdispersion is trivial. By the way, if you really want to assess goodness of fit, you should be using method=laplace rather than the default pseudo-likelihood method. That way, you will get a likelihood on the scale of the data not on the scale of pseudo-data. ... View more

The syntax from Steve is giving a separate block variance for each treatment. For binomial or binary data, there is no residual variance. ... View more

Sorry. FMM is only for fixed effects. One can use NLMIXED, but one must write the code (not trivial). And you won't be able to have as many random effects terms. Here is a good place to get started: http://statistics.ats.ucla.edu/stat/sas/faq/zip_nlmixed.htm The textbook by Walter Stroup on GLMMs is also excellent for this. ... View more

Sorry, I accidentally read "group=" as "subject=". My fault. But this syntax would be more problematical, in my view. You can't model a separate block variance for each combination of treatment and block. Levene's test is continuous data, not binary or binomial. Page 350 of Littell is not about blocks. Syntax comes down to whether the "groups of animals" within the block is the experimental unit or the single animal within the block. Let's assume it is the individual animal. You need a random block effect, and because there is no scale parameter for a Bernoulli distribution, you probably should have a trt*block random effect. Stroup writes a lot about this in his generalized linear mixed modeling book. I would use: random int trt / sub=block; equivalent to: random block block*trt; The subject= convention is more efficient. "Int" is the intercept, basically a column of 1s. So, the first statement is giving you both block and block*trt. ... View more

Steve gives good advice, but I will add some comments. It shouldn't matter if you put binomial or binary, since the Bernoulli is a special case of binomial when n=1. I don't understand why you would use random block / sub=block*trt; Having block on both sides of / does not make sense. Are you trying to get separate random effects for block and for block*trt? If so, then you would use random int trt / sub=block; or random block block*trt; Use of the subject syntax is more efficient computationally. If you just want block*trt, then use random int / sub=block*trt; or random block*trt; There is another difference between the two approaches (events/trial vs event [0,1]). You must make sure that you are properly accounting for the experimental units. If treatments are applied to groups of individuals (say, plants in a pot), and pots assigned to different treatments is random, then the pot is the experimental unit, not the plant. Your first syntax is appropriate then (with my corrections), with the smaller denominator df. Your second syntax would be incorrectly considering each individual (say, plant) as an experimental unit, with plants (not groups of plants) randomly assigned to treatments. ... View more