I'd say your experimental design thinking is a bit murky.   It is important to clearly distinguish between an experimental fixed effects factor and the experimental units (i.e., random effects factor) to which the levels of the fixed effects factor are randomly assigned.    As an example, let us say that you have 3 types of well contamination; this is the experimental fixed effects factor with 3 levels. To replicate the effect of contamination type, you "randomly" assign each level of contamination to 4 individual wells; wells are replicates == experimental units == random effects factor with 12 levels (because you have 3 x 4 = 12 wells). Obviously, a factor with 3 levels cannot be identical to a factor with 12 levels. Plus one is a fixed effects factor, and the other is a random effects factor.   In your study, you could think of block as the experimental unit for the well factor (with 3 levels), but then you have no replication and you can do no statistical test. The two factors (block and well) are identical and cannot both be included in one statistical model.   If you are thinking of well as a fixed effects factor and you want a statistical test of whether the 3 well means are equal, then the only thing you can do is to use the duplicate samples as replicates. The duplicate samples need to be independent draws of water from the well to function even minimally as replicates, so that the draws represent a random sample of all possible draws you could have made from that well on that date.    If that assumption seems untenable, you could consider using methodology for unreplicated experiments. See Chapter 5 in this text by Milliken and Johnson:   https://www.amazon.com/Analysis-Messy-Data-Nonreplicated-Experiments/dp/0412063719   where their sausage type is your well, and their judge is your date. This method is not a perfect solution, as discussed in the book, but might be preferable to assuming that your duplicate samples function as true replicates. ... View more

So, "block" is the same thing as "well", just a different name?   You have 3 wells and 4 dates, but 24 observations. What accounts for 24 observations on 12 treatment combinations?   If you incorporate date as a categorical factor, you need a design (experimental/sampling) unit that serves as a replicate for each level of well. It's not obvious what that is so I doubt you have a correct model yet. ... View more

Show us the code that you've tried so far.   ... View more

Check the Model Information table to see what estimation method was used. A model with a random statement and a non-normal distribution will use a pseudo-likelihood method by default http://documentation.sas.com/?docsetId=statug&docsetTarget=statug_glimmix_details66.htm&docsetVersion=14.3&locale=en and by default IC statistics are not computed for pseudo-likelihood http://documentation.sas.com/?docsetId=statug&docsetTarget=statug_glimmix_details76.htm&docsetVersion=14.3&locale=en   Ideally, the distribution of choice would be logically consistent with the inherent nature of the response. The lognormal distribution is appropriate for a response measured on a continuous-scale. The negative binomial response is appropriate for a count response. What is cDNA, what is its measurement scale, and what range of values does it take? "gene copy numbers" suggests a count.   Is "date" measured repeatedly on the same "well"? How many dates are there? We would benefit from a more detailed description of your study design.   I do not like the looks of your RANDOM statement. Generally, you would not use "random _residual_" for a negative binomial distribution because the negative binomial distribution already and implicitly estimates a scale parameter. To be honest, I have no idea what the impact of  " / subject=well" would be. I'm guessing not good, but I could be overlooking something. From where did you get this syntax idea? (If it came from an example assuming a normal distribution, then it is not applicable to a negative binomial distribution.) If date is a repeated measures factor, then you can use a GLMM or a GEE, but you have to choose one or the other and specify appropriate code syntax.   An excellent resource for GLMMs (and to a lesser extent GEEs) in SAS is the text by Walt Stroup https://www.amazon.com/Generalized-Linear-Mixed-Models-Applications/dp/1439815127/ref=sr_1_1?ie=UTF8&qid=1512020181&sr=8-1&keywords=stroup+mixed+model (It would be an excellent holiday present.) These are complicated, persnickety, and treacherous models; and attempting them casually usually is asking for trouble.    Apart from the fact that I do not like your current model...the zero values for Generalized Chi-Square and Gen.Chi Square/DF could be just rounding. Note that the Estimate for Residual in the Covariance Parameters table is very small.   ... View more

Excellent! Thanks for letting me know. ... View more

Please provide more detail. See the posting guidelines here:   https://communities.sas.com/t5/Getting-Started/How-to-get-fast-helpful-answers/ta-p/226133/jump-to/first-unread-message   and here   http://support.sas.com/resources/papers/proceedings12/189-2012.pdf   In particular, post the full code for the statistical model, and show what you've tried so far.   ... View more