You're welcome. You can always post follow-up questions in the future!   ... View more

As you learn more about the basics of experimental design, keep in mind that a fixed effect (like TRT) cannot also be an experimental unit. EUs are random effects factors. Levels of treatment are randomly assigned to experimental units; to have replication, you must have more experimental units (i.e., more levels of the random effects factor) than treatment levels. In my experience with clients, I've found that this distinction is critical to understanding design.   Other excellent resources are SAS for Mixed Models, 2nd ed Generalized Linear Mixed Models: Modern Concepts, Methods and Applications particularly Ch 2, 7, and 8   If I understand your design correctly, this is how I envision it:   REP is the random experimental unit for the fixed effect of YEAR. There are 4 REPs in 2015 and 4 different REPs in 2016. Plots within REPs are random experimental units that are  randomly assigned to 8 treatments, which are comprised of a 4 x 2 factorial (hybrid x seeding). 10 corncobs are randomly chosen from each plot. The same 10 corncobs are measured at each of nine times. The values for the 10 corncobs are averaged for each TIME.   I would consider this analysis:   /* Check pattern of observations */ proc tabulate data=weekly_moisture; class year rep trt time; table trt*time, year*rep; run; /* Visual assessment of raw data */ proc sort data=weekly_moisture; by year rep trt time; proc sgpanel data=weekly_moisture; panelby year trt / columns=4; series x=time y=moist / group=rep markers; run; proc sgpanel data=weekly_moisture; panelby year rep / columns=4; series x=time y=moist / group=trt markers; run; /* Add factors to dataset */ data weekly_moisture; set weekly_moisture; if trt= 1 then do; hybrid= "H1"; seeding= "Early"; end; else if trt= 2 then do; hybrid= "H2"; seeding= "Early"; end; else if trt= 3 then do; hybrid= "H3"; seeding= "Early"; end; else if trt= 4 then do; hybrid= "H4"; seeding= "Early"; end; else if trt= 5 then do; hybrid= "H1"; seeding= "Late"; end; else if trt= 6 then do; hybrid= "H2"; seeding= "Late"; end; else if trt= 7 then do; hybrid= "H3"; seeding= "Late"; end; else if trt= 8 then do; hybrid= "H4"; seeding= "Late"; end; run; /* On original percentage scale */ proc glimmix data=weekly_moisture(where=(moist < 100)) /* typo? */ plots=(studentpanel boxplot(fixed student)); nloptions tech= nrridg; class rep year hybrid seeding time; model moist = year | hybrid | seeding | time; random intercept / subject=rep(year); *random intercept / subject=seeding*hybrid*rep(year); /* this statement is optional for ar(1), should be omitted for most other types */ random time / subject= seeding*hybrid*rep(year) type= ar(1) residual; lsmeans hybrid*seeding*time / plot=meanplot(join cl plotby=seeding sliceby=hybrid); run; /* logit transformation of percentage */ proc glimmix data=weekly_moisture(where=(moist < 100)) /* typo? */ plots=(studentpanel boxplot(fixed student)); nloptions tech= nrridg; class rep year hybrid seeding time; moist_logit = log(moist/(100-moist)); model moist_logit = year | hybrid | seeding | time; random intercept / subject=rep(year); *random intercept / subject=seeding*hybrid*rep(year); /* this statement is optional for ar(1), should be omitted for most other types */ random time / subject= seeding*hybrid*rep(year) type= ar(1) residual; lsmeans hybrid*seeding*time / plot=meanplot(join cl plotby=seeding sliceby=hybrid); run; Because the response is a percentage, you could consider a beta distribution (which is a generalized linear model); however the beta distribution does not work well when modeling different covariance structures for repeated measures. I've included a logit transformation in the code as an alternative, but it makes little difference with these data.   You could think about regressing on TIME.   You could think about other covariance structure types. You may run into convergence issues because of the minimal variability of the response.   Be sure to check weird data (e.g., a response value greater than 100).   You have so little variance in your data that you'll get a lot of significant effects. As you interpret your results, keep in mind that this is statistical significance, and not practical significance.    ... View more

Thank you for the additional information. I hope you are feeling better!   Because this is a field experiment and because the treatment is a combination of corn hybrid and seeding date, the experimental unit almost surely is not a corn cob; rather it is probably a plot or a site or a field--in other words, some spatial unit that was planted with a particular hybrid at a particular time: each experimental unit is a set of corn plants associated with one level of treatment. How are these experimental units (plots? sites? fields?) arranged in space? Are they clustered into sets (i.e., blocks) or is each EU independent of every other EU? You seem to have an inadequate understanding of the principles of experimental design. My favorite reference on this topic is  Statistical Principles for the Design of Experiments. Yes, it's an entire book, but experimental design is a big topic.   Please describe the physical layout of your experiment in space with respect to treatments in each year.   I do not think your model is correct yet.     ... View more

The information I'm seeking is what you would provide in a Methods section of a manuscript. (You have to write it eventually, you might as well do it now.) My rule of thumb is that the Methods description should allow a reader to duplicate your study. What you have provided is not yet enough, so more questions :   This a field study or a lab study? What are your TRTs? What is the experimental unit to which a level of TRT is randomly assigned? What is a REP? I want to know how a REP relates to a corn cob, or clusters of corn cobs. Is a REP the experimental unit to which a level of TRT is assigned? Or is it a block of experimental units? Is each value of MOIST measured on one corn cob, or is it the mean of 10 corn cobs? I'm trying to figure out where "10 corn cobs" works in here.  Is MOIST a percentage? What is TIME (e.g., days?), and what are the levels of TIME? Are the levels equally spaced? Do you measure MOIST on the same corn cob nine times, or do you use a different corn cob each time? Do you use different corn cobs in different years? Do you use different REPs (whatever they are) in different years? Do you use different experimental units for TRTs in different years? Within each year, are all four REPs run simultaneously or do you run one REP to completion, then the second, then third, then fourth? Within each REP, are all eight TRTs run simultaneously or sequentially?   Your MOIST values are very similar among REPs (i.e., there is very little variability), apart from some notably odd values which might be typos or outliers. In my experience, agricultural data are typically quite noisy, so your data are uncommon in this regard.   ... View more

You said you were measuring corn cobs. But to set up a correct model, I need to know what comprises a block, and what comprises a rep. I also need to know whether you have different blocks and reps in the two years: was the same rep followed across two years, or did you have new reps in the second year?   In other words, I need a more complete description of your experimental protocol.   I'd say you are understating the importance of random effects. Replications are random effects, and they are critically important in defining the inference space of your study. Year can be random or fixed; in my opinion, with a small number of years (e.g., 2) in field experiments you are better off thinking of year as fixed, not random. It's an arguable point, though.   ... View more

The "subject" is the design unit on which repeated measurements are made. It should be a random effects factor, which TRT is not (TRT is a fixed effects factor).    I don't have a clear sense of your experimental design, so I'm not going to speculate what the appropriate subject might be. The appropriate subject will involve REP, but YEAR might play a role as well, and you have not clearly identified the role of YEAR in your study. Is YEAR a fixed effects (and so affects the mean of the response) or is it a random effect (and so affects the variance of the response)?   The appropriate subject specification also depends upon how factors--notably REP, in your case--are coded. Keep in mind that you are providing information to the PROC: you are identifying a random effects factor and its levels. When reps are coded the same for all levels of TRT (as in your data set), you need to specify more than just REP to tell the procedure that you have different REPs for different levels of TRT: think REP(TRT).    ... View more

If the response is normally distributed, then it is possible to specify the same model in MIXED and GLIMMIX.    In the code you provided, you specify two different statistical models: the structures of the fixed effects components are the same, but the structures of the random effects components are different. And "subject=trt" is wrong. These issues suggest that you may not have an adequate understanding of mixed models, your experimental design, and how to specify it as a mixed model. I recommend studying SAS® for Mixed Models, Second Edition, and then following up with any questions. ... View more

Your current codes do not match the description of what you planned.   The methods in your dissertation proposal describe a model that linearly regresses a response variable on both SLC and TRIAL1, with random coefficients. Both of these variables are ordered, so regression is a plausible approach. But because SLC and TRIAL1 are in the CLASS statement of your SAS codes, the models specified by your SAS codes treat SLC and TRIAL1 as classification (categorical) factors, so when either SLC or TRIAL1 or both appear in the MODEL statement, you get an ANOVA model, not a regression model.     Everyone starts learning statistical methods knowing nothing at the beginning. The modeling options for your study design are relatively complex, and your current understanding of these models is still very limited. You can certainly learn to do these models correctly, but there is a lot to learn, too much for me to take you through that process in this SAS Community forum. I highly recommend that you find help at your institution from a statistical consultant or faculty member, in addition to self-study and/or additional classes. These are wonderful tools for you to have at your disposal in the future, but these tools take work to acquire. Good luck and have fun!   ... View more

By "pertinent contrast" I mean a linear combination of means (in other words, a contrast) that addresses a sensible (in other words, pertinent) comparison. With respect to a significant interaction, you must ask yourself, "What comparison(s) should I make to figure out the nature of this interaction?" My previous point was that pairwise comparison of interaction means typically is not sufficient for this task (unless the interaction is 2 x 2).   You can, of course, add statements to obtain additional output, like estimates of main effects or of simple effects. The code I suggested is just that--a suggestion. You are free to use it or not, or alter it to suit your needs.       random intercept / subject=trial1(subjectid group); estimates the variance among multiple trials within subjects. You confirmed in a posting that you subsequently deleted that trials are, in fact, intended to be subsamples and that you have no research questions about the effect of trials on the mean of the response. TRIAL1 is a design unit that is nested within each SUBJECTID within each GROUP.   You could apply a simpler statistical analysis if you computed the mean of the response over the multiple trials for each syllable-set for each subject in each group, and then used those means as data in a simpler statistical model (a two-way factorial in a split plot design). If you had the same number of trials for each subject in each group, you would get the same test results with this analysis using a data set with observations at the subject by syllable-set level as you would with the analysis that uses a dataset with observations at the trial by syllable-set level (in other words, your current data set structure). However, you are missing data for some trials, so the results of the two approaches will not be identical for this study. The analysis using your current data set structure with a more complicated statistical model is (ideally) better, but for practical purposes, the simpler one may well be good enough.    But you also said in the deleted post that "I am willing to see any effect of "trial" as a side question. There can be learning effect." which implies that TRIAL1 must be included as a fixed effects factor in the MODEL statement in some form. As the research scientist, you need to decide which approach you are taking to the role of TRIAL1 in your study. Ideally you would have determined this during the design phase of the study, before you actually ran trials.       random _residual_ / group=syl; Study Ch 9 "Heterogeneous Variance Models" in SAS® for Mixed Models, Second Edition. If you still have questions, feel free to ask again. The RANDOM _RESIDUAL_ combination in GLIMMIX replaces the REPEATED statement in MIXED.     ... View more