As PGStats stated, the Poisson distribution is for counts. But your "counts" are decimal values. You must have converted the raw values to some unit scale (volume, etc.). One can do the analysis on these decimal values, but first you want to make sure you really are analyzing counts.
In the procedure code you supplied, you took the fairly common approach (and generally recommended approach) of modeling the log(ExpectedCount) as a linear function of the treatment factor. That is, you told the program to use the log link (which is actually the default for the Poisson). Note that in generalized linear (mixed) models, one models the log of the expected value, not the expected value of a log of the variable (as one would do with transformed Y and normal distributions). The statistical results are all on the log-link scale. That is appropriate. But you also gave the inverse link option; this means that you are also getting the mean counts and confidence intervals on the original scale (just to the right of the log scale results in the LSMEANS output table).
The default model fitting approach in GLIMMIX with random effects is known as pseudo-likelihood or pseudo-restricted-likelihood. This prevents you from easily evaluating goodness of fit. (I can't get into the technical details here, but in short, the model is being approximated, which prevents direct interpretation of the likelihood obtained). There are some work-arounds by saving certain results and doing some post-model-fitting analyses. For your model, however, there is a better and more direct approach: use a model fitting method that works without approximating the model. I suggest you use the Quadrature method (method=quad). You must write the random statement in a different way (but equivalent in terms of meaning and interpretation. That is, use
random int / sub=blk;
instead of
random blk;
.
Full code:
proc glimmix data=abundancevisit3 method=quad;
class trt blk;
model y = trt / dist=poisson link=log;
random int / sub=blk;
lsmeans trt / cl ilink;
run;
Now you get a proper Pearson chi-square statistic and df (and the ratio) to help in evaluating the model fit. For your example, the ratio is under 1; thus, no evidence (from this statistic) of a poor fit. The model is still log(Exp.Count) as a function of treatment. The ilink option gives the means and other statistics on the original scale.
Good luck.
LVM
can advise you on the robustness of the analysis to departures from the Poisson distribution. GLIMMIX offers you the negative binomial as an alternative distribution for counts.
