Kudos for a well-crafted question. I wish I had the answers to all of your questions.    1) Is the baseline covariate parameterized correctly in the model statement? Do I need both the NO3 cov and NO3cov*Sample_Date to account for the fact that the relationship of the response variable to the covariate changes over time?   I can see the value in using (the mean of the first four dates of) NO3cov as a covariate. I think it would make sense to use log(NO3cov) if you are using a lognormal distribution for Concentration_NO3. The model assumes a linear relationship between the link-scale of the response and the covariate.   NO3cov*Sample_Date allows the slope of the linear regression of Concentration_NO3 (on the link scale) to vary by Sample_Date. You should retain NO3cov if the interaction is in the model statement. 2) Do I need to change or include an additional random statement when I add the covariate? will the df be correct for the covariate effect with the specification that I have?   Adding a covariate into a mixed model is an appreciable complication, depending on the hierarchical level at which the covariate is measures (here, Rep*Irr_Trt*N_Trt, aka subplot); check out random coefficient models in the Littell et al. text (SAS for Mixed Models, 2nd ed), Stroup (Generalized Linear Mixed Models), and Milliken and Johnson (Analysis of Messy Data, Vol III Analysis of Covariance).   I always go into a model with some idea of what I think are appropriate denom df, just to check. 3) How does the inculsion of the covariate affect the existing repeated measures covariance structure?   Not sure about that. 4) Is this even an appropriate use of a covariate?   Google "change in baseline ancova". 5) Is it a "problem" that the main effect of NO3cov is not significant while the interaction effect of NO3cov*Sample_Date is? What about the increase in AICC value when the covariate was inculded?   Nope. Google "ancova centering". This text https://books.google.com/books/about/Multiple_Regression.html?id=LcWLUyXcmnkC has a nice introductory level discussion of centering.   Regarding the AICC increasing with the inclusion of the covariate: To compare models that differ in fixed effects factor, you need to use a true maximum likelihood method (LAPLACE or QUAD), rather than REML.     There are many possible different bells and whistles to be considered. Is the relationship linear? Does the slope vary with Irr_Trt and/or N_Trt? Is the slope constant for all whole plots, or does it vary?    Stepping back further, I would ask: What is your research question about sampling dates? 21 or 25 levels is a lot to sort out in an ANOVA context. Why did you make all these observations? Are you actually interested in comparing means among all 21 or 25? Would it make sense to extract some agronomically meaningful statistic from all these measurements to use as a response, or to regress on sampling date? Is there a statistician at your institution that you could work with, or a statistics prof, or a statistical consulting center? (I know, there may not be anyone, or at least anyone that knows more than you.) Lots of things to ponder, and a good stat colleague would be a more useful thing than this forum. ... View more

Your model is a multiple regression with 27 predictor variables.    I would look at   (1) whether there is enough data to to support the estimation of 27 parameters; for example, if your sample size is 20, then this model is overparameterized (having "Infty" df suggests overparameterization), and   (2) whether there is multicollinearity among the 27 predictors   (3) whether you have the correct model for your study design ... View more

I would not say that dad and mom as random effects factors have an effect on the intercept. Random effects factors affect the variance of the response variable, but not the mean of the response variable (and the intercept is the overall mean). I'd give this objective more thought.   The COVTEST syntax is the same regardless. It's all about the order of the covariance parameter estimates.   If you have a continuous covariate (JSH) measured at the individual offspring level, then you will have to embed that regression in a mixed model because offspring are nested with matings. Be sure you look at plots of the data to assess linearity (on the logit scale for the binary distribution), look for influential observations, etc.   Particularly if you are planning to add more covariates to your model, you should seek out a statistician at your institution/company with whom you can discuss statistical issues vis-a-vis your study issues.  ... View more

Several thoughts...   1. Sex is not a random effects factor; it is fixed. I recommend http://onlinelibrary.wiley.com/doi/10.2307/1941729/abstract for its articulation of what is fixed, what is random, and what is hard to decide.   2. For similar studies in the future, I would ponder a different design with respect to allocation of animals of different weights to treatments. Blocking is very crude (you lose all that information about individual weights by lumping five animals into the same group), and you are measuring weights anyway, so think about using initial weight as a covariate. Even better, consult with a statistician at your institution/company (if one is available) about design possibilities.   3. I recommend not applying Type I error adjustment within the LSMEANS statement to pairwise differences among interaction means, because many of the comparisons are not sensible (e.g., A1B1 to A2B3). You lose too much power that way. Pairwise comparisons among main effects means are fine.    4. Assuming that I understand your design correctly, I would consider proc mixed data=have; class wtblock sex trt day; model bwkg = sex | trt | day; random wtblock(sex); repeated day / subject= trt*wtblock(sex) type=<whatever>; run; where <whatever> is CS or AR(1) or such, but not UN: your sample size is most likely too small to support all the covariance estimates (depending upon the number of DAYs). Along with the MIXED documentation on covariance structure types, I recommend  http://onlinelibrary.wiley.com/doi/10.1002/1097-0258(20000715)19:13%3C1793::AID-SIM482%3E3.0.CO%3B2-Q/abstract   To implement the AR(1)+RE structure described in the above paper, you would include random trt*wtblock(sex); Few other covariance structures include that term. ... View more