@Nicheca,  If ANIMAL is coded 1 to 20 within each TRT level, then you must use subject=ANIMAL(TRT) so that GLIMMIX can recognize 40 animals rather than 20. If ANIMAL is coded 1 to 40, then you could use either subject=ANIMAL or subject=ANIMAL(TRT) but the second syntax will generally do a better job at estimating denominator df, in my experience.   I prefer this syntax; I am remembering that it's safer to use in case you do not have all locations for all subjects or the data set is not sorted by location within subject (but I can't find a reference for that quickly).   random location / subject = Animal(TRT) type=cs residual; TYPE=CS is a homogeneous variances structure (as well as homogeneous covariances/correlations, as noted by @cminard ) so if you have a balanced design you will get the same SE for all estimates of a similar type (for example, pairwise comparisons among locations). You could try other covariance structures that allow heterogeneous variances (for example, heterogeneous compound symmetry CSH or UN) and see whether any provide a better fit to the data, and you could do graphical assessment of residuals to see whether those indicated heterogeneous variances among locations (I use boxplots).   I hope this helps. ... View more

You usually will want to have COW in the CLASS statement.   Is it possible to put MONTH and AGE in the model? I don't know. What happens when you do? (And is it reasonable to assume a linear relationship between MP and MONTH or AGE?)   If you get errors, or 0 Den DF, or missing p-values, or some other pathological output, then there is some conflict between MONTH and/or AGE and/or TREATMENT|PO|DL. Without knowing more about the structure of your dataset, I cannot say what the problem might be.   ... View more

A common cause for DenDF=0 and consequently Pr>F = . is that the model is overspecified in some way.    You have not provided enough detail about your experimental design to allow me to be any more specific. Some aspects are not clear: 1) DL takes values from 1 to 60, which span two months. You also have a MONTH factor. How are DL and MONTH related? 2) Multiparous cows are likely to be consistently older than primiparous cows; multiparous cows probably have a range of ages, but primiparous cows might not, and the ages of the two groups might not overlap. How are PO and AGE related? Presumably a cow is either primiparous or multiparous? 3) The Num DF for DL is 3, when you expect 6 (=7-1).  This could be a coding problem, or some overlapping redundancy with MONTH. 4) How are AGE (measured in months) and MONTH related?  5) Is it reasonable to assume that milk production is a linear function of MONTH and AGE?    I find it helpful to use the TABULATE procedure to look at the data set structure, for example   proc tabulate data=<yourdataset>; class dl month po age; table dl, month; table age, po; run; If you would like to post more information (including an example dataset that has the same structure as your dataset), then someone in the Community might be able to provide more insight.   ... View more

The design planning process described in Stroup's paper works for any statistical model that you can specify using either the MIXED or GLIMMIX procedures. So if you can write a statistical model for your crossover design, then you can estimate sample sizes for specified exemplary datasets. That's the beauty of this approach: it can deal with a wide variety and complexity of statistical models. Although, of course, the process gets more involved as the statistical model gets more complex.   I do not know of any papers describing this process for a crossover design, but that does not mean that there are none. I suggest starting simply, with "subsets" of your design--for example, an assessment of sample size for just the first period if you have replicate subjects--and then build from there.   I hope this helps.   ... View more

It sounds like you might have found a "good enough" model 🙂   If you have a decent idea of what the denominator degrees of freedom "should" be, then you can specify them explicitly with the DDF option on the MODEL statement.  ... View more

(For those of you who saw my prior post: I misunderstood the OP's reply, so I have edited. Use this one instead.)   I also have doubts about the correct model, and I do not have enough information about your research questions to do much speculation.   The dilemma of collapsing observations within each year to months is that a monthly basis is arguably arbitrary. How do you justify collapsing to a month level? How do you justify the date cutpoints that determine "month"? Trees do not recognize the human concept of "June" versus "July", for example. Is "June" in year 1 equivalent to "June" in year 2 equivalent to "June" in year 3? In the field, this is not usually the case because of annual variability in weather. Should year be a factor that is separate from month?   When in doubt, go back to your research questions. Why did you measure over 3 years? What did you expect to learn from the temporal observations within each year? What did you expect to learn from the observations over multiple years? What aspect of these temporal observations is fundamental to your research questions? For example, perhaps you are primarily interested in annual growth and care less about the growth within each year.   34 observations per tree (= 3 x 11 plus an extra? = 3 x 12 minus 2?) is still a lot for an interpretable ANOVA. I'd give it more thought. If you have statistical consultation available to you at your institution, take advantage of it, particularly if the consultant has some familiarity with your discipline.   I hope this helps.     ... View more

The question that you cite is ill-posed and cannot be answered as written:  If you have a 3x2x2 factorial, you have MANY comparisons that might differ by at least 30 ppm. Which pair of the 3 levels of factor A (temperature) differ by at least 30 ppm? Do the levels of factor B (humidity) or C (age) differ by at least 30 ppm? Do comparisons within interactions differ by at least 30 ppm? Do ALL comparisons in the entire model need to differ by at least 30 ppm?   Even if your statistical model is not mixed, you can use the GLIMMIX procedure to determine sample size in complex models, by using exemplary datasets. (GLMPOWER also uses exemplary datasets.) An exemplary dataset represents an alternative hypothesis for which you would like to assess power--it is what you think the mean structure of your data will look like, and it replaces actual data in the procedure. Once you understand the concept of exemplary data, you'll see why you do not need an actual set of data.   For a 3-way factorial, coming up with an exemplary dataset is a nontrivial problem requiring much thought and a good familiarity with the context of the study, because you have to envision the entirety of the 3-factor outcomes of interest (so, really a set of alternative hypotheses: effect of A and effect of B and effect of C, and interaction of A and B, etc.). See PROC GLIMMIX as a Teaching and Planning Tool for Experiment Design for an example of the process.   For your question, I might imagine that the 30 ppm applies to the difference in age. But what if the difference in age is not expected to be the same for all temperatures and humidities? Then you need to assess power for interactions and it gets more complicated.   I hope this helps.   ... View more

I would use GLIMMIX.   60 repeated measurements on each plant is a lot. You could specify an ANOVA model for repeated measures in time, but interpretation of the interaction of treatment and time will be challenging. I suggest that you give some thought to what you want to learn about the response over time--in other words, why did you take 60+ observations on each plant? You might be able to reduce the number of time levels (for example, you mention period as a factor). Or, a better idea of your research questions about response over time might suggest alternatives for a statistical model, for example, incorporating a regression on time (e.g., an ANCOVA type of approach).   This book would be an excellent resource.   I hope this helps.     ... View more

Hmm.   I don't see that your model is overspecified (resulting in 0 ddf for some terms), although there could well be something I don't see or some data structure that I don't know that. So at the moment I can only offer some thoughts and questions.   Does each tree have the same DAP for all years, or does DAP change with year?   Have you tried centering or standardizing DAP?    What proportion of the prod values are equal to zero? Might zero values be predicted by your explanatory variables? Would it be worth ignoring the mixed model structure and exploring a mixture model (e.g., zero-inflated or hurdle) using the FMM procedure? https://documentation.sas.com/?docsetId=statug&docsetTarget=statug_fmm_gettingstarted02.htm&docsetVersion=15.1&locale=en     ... View more

I think you will have more flexibility with the GLIMMIX procedure with a judicious use of likelihood ratio tests of nested models, some of which can be implemented with the COVTEST statement and others which you'll have to do yourself. For example, you could fit one model with a common variance for methods and compare to a second model with separate variances for methods to test equality of variances. (You could take this approach with MIXED as well.)   GLIMMIX does not allow use of Kronecker products, but I don't see that as much of a problem because there are other modeling options. Advanced Techniques for Fitting Mixed Models Using SAS/STAT® Software (examples on page 5) may be illustrative. The GROUP option on the RANDOM statement might be useful.   I don't know of a way to get an F-test and a CI on the difference of variances directly from MIXED or GLIMMIX. I suppose you could bootstrap CIs. Or perhaps someone else in the Community has an idea.   This is an ambitious effort. Good luck!   ... View more

You can use the GLIMMIX procedure for this purpose. See PROC GLIMMIX as a Teaching and Planning Tool for Experiment Design.   I hope this helps.   ... View more

I cannot tell what you want with respect to question 3, but that aside, I would consider a mixed model logistic regression, which will definitely address Q1 and Q2. For an example, see Multilevel Models for Categorical Data Using SAS® PROC GLIMMIX: The Basics or Hierarchical Logistic Regression Modeling with SAS GLIMMIX .   I hope this helps.     ... View more

You could consider a structural equation model; for an example, see Implementing structural equation models to observational data from feedlot production systems.   ... View more

Have you looked at the COVTEST option on the PROC MIXED statement?   The example in Analyzing Multivariate Longitudinal Data Using SAS® appears to be similar to your study.   I hope this helps.   ... View more