An offset of 0 is a perfectly valid value for the offset. With a log link, it is interpred on a log scale. Log(x)=0 is perfectly valid, because it means that x=1. So you are modeling 0/1, not 0/0. ... View more

The chi-squared statistic in the output is just the Wald statistic, (estimate/SE)^2. The square root of the chi-squared statistic for a single parameter estimate is just the t statistic (with infinite denominator df).  ... View more

I just tried my example with a ZIP model and I get the same results if I take out the observations with a missing for the offset or if I just using the missing value for the offset. So, I don't see a problem. A response count of 0 is a perfectly valid number for the Poisson or Negative binomial; it is only the offset that matters here. ... View more

I am not sure where the problem lies. I just tried a similar approach and all worked just as expected. If you use an offset of missing (that is, log(0)), that observation is indeed missing in the analysis. I get the same results by removing the missing offset observations or by using simply using missing (.) for the offset. Using missing offset, GENMOD correctly indicates that some values are missing. I was using a Poisson distribution. I think your problem is with the zinb distribution. As far as I can tell, the offset is used only in the model defined by the MODEL statement. I have not investigated this, but I am guessing that the link is not used with the ZEROMODEL If that is the case, the observations with offset=. would still be used for some of the model fit. ... View more

The zinb model in GENMOD is not a hurdle model, but a more general mixture model. The defined model includes the zero term; then you have the added zero component term (a distribution defined only at 0). The probability of 0 is related to the sum of the probabilities from the model statement and the zero term statement. If you fit just a null model, you would not get the same results.   In your first FMM run, by using a trucated NB, you are not getting the probability of 0 for the first component. Thus, it is a different model. ... View more

KR is for normal data. ... View more

SAS is committed to the Kenward-Roger (KR) degree of freedom adjustment for the linear model problem. You can read about it in the documentation for MIXED or GLIMMIX. It is not available in GLM. KR is recommended for analysis of covariance. The book SAS for Mixed Models, 2nd edition (2006) demonstrates in detail. ... View more

The problem is your treatment of X as a parameter. I tried this with some data, and MCMC cannot mix. If you just had a model with X_mu as the predictor variable, it runs fine. Of course, you may have a reason to treat the predictor as a variable, although I am not aware of a reason for doing so. ... View more

You are not getting any mixing at all in the chain. Your profile plots must look very strange. It is probably related to the fact that you do not have a free residual variance parameter. You are fixing the standard deviation (variance) at a constant in the model. This usually is a parameter with a prior. I don't know why you are treating X as a parameter rather than as a fixed predictor variable. I assume you have a good reason (perhaps, as a measurement-error model). ... View more

Several versions of pseudo-R2 statistics have been proposed for generalized linear models (GLMs). Here is one developed in the 1990s by Cameron and WIndmeijer and by Waldhor. You need to run the procedure twice, once with the covariates (predictor variables, factors) and once without any covariates. Get the Deviance for each model fit (it is printed). Then, pseduo-R2 = 1 - [Dev_full / Dev_red] where Dev_full is the deviance for the full model (with all the predictors), and Dev_red is the deviance with no predictors. The argument for this R2 comes from the equivalence of deviances and sums of squares for linear models. You can read more about other approaches in Heinzl and Mittbock (2003; Computational Statistics and Data Analysis 44, pages 253-271). ... View more

Be careful. You are in dangerous territory. Your idea of deleting only the largest observations (or the smallest, but not both) can lead to arbitrary results. Rick has a better suggestion: use various robust statistical methods that deal with extreme observations in an appropriate manner. I highly recommend the quantile regression procedure. Primarily used for relationship between variables, it can be used for many other robust statistical estimates. I think Rick has a blog post on this. ... View more

Good point. It is interesting that it takes about the same amount of time with MEANS as with HPSUMMARY to get quartiles (P2 option) on 50 M observations (on my desktop). ... View more