One more bit of input:   Here are some analysis ideas for your study. 1. Define two blocks (rep), one for the main plots first measured in 1994 and a second for main plots first measured in 1995. Block variability will include both spatial and temporal sources. See link to Loughin paper below. 2. Define a new variable (year_order) that takes values 1 through 6 (1 for 1994 and 1995, 2 for 1996 and 1997, etc.) This will prevent problems due to an incomplete factorial. 3. Fit a mixed model with year_order, something like (untested, of course):   proc glimmix data=<>; class rep rot till year_order; model y = rot | till | year_order / ddfm=kr2; random intercept rot / subject=rep; random year_order / subject=rep*rot*till type=<> residual; run; 4.  Replace year_order (which is categorical, hence ANOVA-like) in the statistical model with date (which is continuous, hence regression). As I mentioned previously, you will not have success including both year and date as fixed effects factors in the same model because there is a one-to-one correspondence between these two variables; and besides, the point is to replace year with something more mechanistically informative. As you work through this analysis, you can now consider (1) whether the relationship between y and date is linear; (2) whether and how to center the covariate (you'll want to center the covariate, but you'll have to decide which value to center on; see link to paper below); (3) whether to incorporate random slopes; (4) whether to incorporate autocorrelation among the repeated measurements within each subplot; (5) and probably other stuff that pops up during the process (e.g., distributional assumptions, variance estimation problems). Hopefully you are now a bit apprehensive about the complexity of this process, and that's good. It is complicated, and that's why a good stat consultant is so valuable. This is not a do-it-yourself project for most people who do not have extensive stat experience.   You'll find design insight in this paper by Tom Loughin Improved Experimental Design and Analysis for Long-Term Experiments. His setup is not exactly like yours (it has observations on each experimental unit in each year), but you'll find concepts and parallels for your study.   For random slopes and centering, particularly centering on values other than the overall mean, this paper is good A simple method for distinguishing within- versus between-subject effects using mixed models.    I hope your on-campus resources work out for you. Good luck, and enjoy the process!   ... View more

I think the full factorial is incomplete because each Main is not measured in each year, and there are only two reps (Main) for each ROT x TILL combination. So I'd look at   proc tabulate data = <>; class rot till year; table rot*till, year; run; or   proc freq data = <>; tables roc*till*year; run; ... View more

I appreciate the additional information, but there still is not enough detail to identify a statistical model that is consistent with your experiment. Plus crop rotation studies are complicated regardless.   I find that it is extraordinarily useful to distinguish between design components and treatment components in an experimental design. Using your favorite search engine, search on "design structure and treatment structure"; there are several useful hits. You are currently co-mingling the two concepts. For example, you do not take samples from "each ROT and TILL" (of which there appear to be 7 x 2 = 14 combinations); instead you take samples from the experimental units assigned to levels of ROT and TILL, of which there are 14 x however many replications.   You may have statistical support available at your institution, perhaps even within the agricultural academic unit. If so, you would likely find it invaluable to work across a table rather than across the internet.   I hope this helps.   ... View more

If your design is a "standard" two-way factorial in a split-plot design, with whole plots in blocks and with repeated measures, then your use of main in your code looks odd to me. Your problem with including a covariate may be a problem with your basic model specification, and not necessarily with the covariate addition. (Although I'm also a bit suspicious about the role of date when year is in the model.)   Would    proc glimmix data=<something>; class rot till year rep; model NO3=rot|till|year / ddfm=kr; random int rot / subject=rep; random year / residual subject=rep*rot*till type=<something>; run; be more correct for your basic model? (Note that rep*rot -- as implemented in the first random statement -- is an alternative way to identify a specific whole plot, which you might be calling main. Knowing which rep and which level of rot, one can uniquely identify which whole plot.)   I hope this helps.   Edit: How a covariate is incorporated in the statistical model depends on the experimental/sampling unit on which the covariate is measured. The covariate could be measured at the whole plot level, or at the subplot level, etc. You're more likely to get better input from the Community if you provide more information about your experimental design. For example, I'm guessing that date (and gdd) are repeated measures made within each year; if so, then when you add date, you need to modify the random statements accordingly. You might find Analysis of Messy Data, Volume III: Analysis of Covariance to be useful in sorting this out.   Edit 2: Looking at the tables you posted, it appears that one value of date (or gdd) is paired with one value of year. If that is true, then you cannot have both date and year in the same model--date and year are redundant, and the model will be overspecified. You have to pick one or the other.   For the future, posting table images is not ideal. Instead, save output to a file, e.g., PDF (not Word) using ODS OUTPUT, and attach the file.     ... View more

This blog post by Rick Wicklin may help you interpret the diffogram.   In my opinion, of the 3 questions you list, only #3 is specified clearly enough to define a statistical model. I don't really know what to make of the other two; I don't find them to be very clearly written. #2 seems to be redundant to #3, and #1 is just puzzling.   The model you posted is not a model I would use to answer question #3.   I hope this helps.   ... View more

Hmm.  To have any more (potential) insight, I would need to see the code for the reduced model, and ideally the full output for both full and reduced models (attached as a file, e.g., PDF, not embedded in your message; as you've noticed, the tables don't embed well).     ... View more

In general, I believe that the statistical model should match the design. In your study, individuals are not independent: they are clustered within families which are clustered within villages. Your model does not appear to be having any trouble with estimation. So I would keep the mixed model.   Other people may have other opinions.   ... View more

Did you include the RANDOM statement in the reduced model?   ... View more

Given your description of your experimental design, some educated guesses that I'm making about your design, and your code snippet, I'd say that you are pretty far off the right track, unfortunately.   If your institution offers statistical consulting, or if you have access to statistically-knowledgeable support staff or faculty, then I recommend that you make use of that. This design appears to have blocking (section?) and subsamples (animals within groups?) and repeated measures (times within periods?), and it likely requires a fairly complicated statistical model, more complex than is really feasible to deal with in this Community forum.    I also suggest learning more about cross-over designs (of which Latin square is an example). Try "crossover design animal science" in your favorite search engine.    I hope this helps move you closer to the right track.    ... View more