Let me see if I understand your experimental design. I am making parts of this up, so correct my description as need be.   You have two years, and you are thinking of year as a random effects factor. You have some (unspecified) number of "blocks" within each year, and you are using different blocks in different years. Within each block, you have one "superplot" (the whole plot unit, and a random effects factor) randomly assigned to each level of the fixed effects factor irrigation (the whole plot treatment). (This is a split-plot with whole plots in blocks, as opposed to a split-plot with whole plots in a completely randomized design.) You have "plots" within each whole plot unit, one plot randomly assigned to each level of the fixed effects factor graft. You measure tomato fruit production multiple times in each plot (16 times in one year, 12 times in the other).   Some thoughts:   1. When I'm sussing out a mixed model, I find it extremely helpful to distinguish between random effects factors (i.e., experimental units) and their associated fixed effects factors (i.e., experimental treatments). For example, the whole plot unit is "superplot" and the whole plot treatment is "irrigation". I deliberately give different names to the unit and the treatment because they are not the same thing. Just saying "whole plot" does not  provide sufficient information.   2. With only two levels, year does not make a very good random effects factor. The model attempts to estimate a variance among years based on the most minimal of data (n=2). For another thing, if year is random and if blocks are nested within years (i.e., different blocks in different years), then one can argue that the inference space for your study is defined by years--year becomes the fundamental replicating factor. With only two years, this is clearly problematic. I'd ponder incorporating year as a fixed effects factor, (randomly?) assigned to blocks. Iit's not always a black-and-white decision.    3. With 16 levels of harvest in one year and 12 levels of harvest in the second year, and if harvest is a classification fixed effects factor, then you have a problem, regardless of whether you use MIXED or GLIMMIX. The irrigation x graft x harvest factorial is incomplete: you do not have data for all combinations of these factors. Consequently, if you include interactions with harvest in your model, some lsmeans will be reported as "non-est" (not estimable); and main effect means for irrigation and graft will be biased regardless of whether interactions are included. You could extract a subset of harvest dates that "match" between the two years (although this exercise may be too subjective to justify adequately). Or you could incorporate harvest as a continuous factor, and regress awtrun on harvest level (i.e., date), which poses additional analysis considerations (e.g., linearity? random slopes?). Or you could combine data over harvests, for example total production for the season and then drop harvest as a factor in the model. Or you could analyze each year separately. Or some other approach that makes sense to you.   4. If response data are normally distributed (conditional on the predictors), then MIXED and GLIMMIX will produce the same results. Syntax-wise, the REPEATED statement in MIXED is replaced by the RANDOM / RESIDUAL statement in GLIMMIX. If you are switching to GLIMMIX to deal with non-normal data, then some modifications to the random parts of the model may be necessary, for example to accommodate overdispersion.   ... View more

Show us the code that you've tried so far. And tell us more about your experimental protocol, especially the order in which the two treatments were assigned to each subject. ... View more

My clients do not have big data sets, to put it mildly, so memory issues are not my forte. I'm intrigued by incorporating random factors as continuous rather than classification. And if that didn't work...there are folks out there that deal with memory issues and I would not hesitate to touch base with SAS Tech Support.   Good luck and have fun!   ... View more

I think I don't like the second RANDOM statement because PATIENT_ID is not the "bottom" unit in the design (i.e. "residual" ); RECORD is. I don't know what you've tried, but this is where I would start:   proc glimmix data=work.dataset ic=q; class geography patient_ID; model outcome_var = a b c d / solution dist=poisson link=log; random intercept / solution subject=geography; random intercept / solution subject=patient_ID(geography); run; If there was evidence of overdispersion, you could add a scale parameter   proc glimmix data=work.dataset ic=q; class geography patient_ID; model outcome_var = a b c d / solution dist=poisson link=log; random intercept / solution subject=geography; random intercept / solution subject=patient_ID(geography); random _residual_; run; or add an observation-level variance   proc glimmix data=work.dataset ic=q; class geography patient_ID record; model outcome_var = a b c d / solution dist=poisson link=log; random intercept / solution subject=geography; random intercept / solution subject=patient_ID(geography); random intercept / solution subject=record(patient_ID geography); run; or switch from Poisson to negative binomial, or to a generalized Poisson.   Speculating wildly and noting that GLIMMIX allows the random-effects to be either classification or continuous (see the documentation for the RANDOM statement in GLIMMIX), you could try incorporating patient_ID (and possibly geography) as continuous effects, i.e., remove them from the CLASS statement. Extrapolating from the documentation for the GROUP option on the RANDOM statement, a continuous random-effect might execute more quickly and use less memory; but I am just guessing here. For sure, you'd have to sort the dataset correctly.   Whoa, 70 variables is a lot. Variables a, b, c, and d are incorporated as continuous variables in your example model, so you're doing linear regression. Lots of challenges: linearity (on the link scale), multicollinearity possibilities, influential observations. You don't identify the level at which these predictors are observed (geography, patient or record). Regression in a mixed model is also known as a random coefficients model; the models above are only random intercepts: they assume that slopes have no random variance. You could assess random slopes--theoretically. In practice, if you are already having memory problems, adding more covariance parameters to the estimation list is not going to make your modeling life easier.   If you try the continous random effects thing, I'd be curious to know how that works out.     ... View more

In your example, DAY is measured on a circular scale: DAY = 1 and DAY = 366 occupy the same position in an annual cycle.    DAY is converted into radian units by 2*pi*(DAY/365). If we define the angle theta as 2*pi*(DAY/365), then we convert from polar coordinates (assuming that radius = 1) to rectangular coordinates (x, y) as x = cos(theta) and y = sin(theta).   The prediction of a linear variable X from a circular variable THETA is known in the circular statistics area as "linear-circular association". From the text by N.I. Fisher https://www.amazon.com/Statistical-Analysis-Circular-Data-Fisher/dp/0521568900 (p 139): "In the linear-circular case, we focus on measuring association between X and THETA with a (possible) view to predicting the mean value of X for a given value theta of THETA. A simple regression model for this type of association has the form ... E(X | THETA = theta) = a_0 + a cos(theta) + b sin(theta) .... it is a simple linear regression model (linear in the regression variables cos(theta) and sin(theta), that is) and can be fitted routinely by methods in any general statistical package, so we shall not discuss the regression aspect further."   I see the use of sin/cos variables applied in ecology to variables like aspect (the continuous version of north-east-south-west). Notably aspect is different than time, and what works for aspect may not be appropriate for time.   So it could be an acceptable way. If you have many years of data, then time series analysis might be an alternative, perhaps better approach. The paper you reference has observations over only two years.       ... View more

Thank you for the clarifications.   I see several issues here.   One issue is inflated Type I error. Notably "Adding sample size to an already completed experiment in order to increase power will increase the Type I error rate (alpha) unless extraordinary measures are taken...." http://depts.washington.edu/oawhome/wordpress/wp-content/uploads/2013/10/Improved_Stopping_Rules.pdf (p 3).   Another issue is that it looks like you have only one realization of the intervention. Although n=1 provides some information, it is merely anecdotal; to demonstrate the impact of the intervention, you would need independent replication.   Another issue is that these observations through time may not be independent, i.e., there may be autocorrelation. Lack of independence reduces the effective degrees of freedom--each observation does not carry a full complement of information. This impacts your assessment of sample size when sample size is the number of observations.   Another issue is the use of statistics derived from the dataset to estimate the sample size desired for that same dataset. This problem is addressed in the retrospective power analysis literature.   So, in summary and in my opinion, although you could retrospectively estimate the number of post observations need to detect a particular effect, the value of that effort is minimal and does not advance your effort to assess the impact of intervention in any meaningful way.    ... View more

The basic methodology is power analysis. This links to a SAS overview  https://support.sas.com/documentation/onlinedoc/stat/142/intropss.pdf   But before diving into specific details about power analysis...   Does your entire dataset currently consist of 10 observations (5 pre and 5 post)? Are you trying to determine how many more post observations you need to achieve a p value less than 0.05?    Or do you have multiple subjects, each with 5 pre and 5 post? And are you trying to determine how many more post observations you need to achieve a p value less than 0.05?    Or are you planning a new study, rather than fishing for significance in the current study?   ... View more

You do have a saturated model: you have 10 observations and your model specifies 10 parameter estimates. You'll have to come up with a new vision for analysis. ... View more

Based on your description of your study, I would say that you have a serious design problem: both SPECIES and TREATMENT are assigned to POOL (i.e., POOL is the experimental unit for these two factors), but you have no replicates of the SPECIES and TREATMENT combinations. You have only one pool for each combination.   If you assume that there is no interaction of SPECIES and TREATMENT, then you could use the 1 df for SPECIES*TREATMENT as the error for testing SPECIES and TREATMENT. Is that a legitimate approach? It depends upon the extent to which there actually is no SPECIES*TREATMENT. And with only 1 denom df, the tests would be of low power.   Unless you are willing to assume that there is no TIME effect and no PART effect, you cannot consider "repetition through time" or "through part" to be valid replications. You clearly think that there may be TIME and/or PART differences, so I doubt that you can find replicates in this fashion, apart from other concerns I would have about the validity of this.   Ignoring the lack of replication problem for the moment.... Plants (aka ID) are clustered within POOLs, and IDs are the experimental unit associated with the TIME factor. At this point, your design resembles a split plot where POOL is the whole plot unit, SPECIES and TREATMENT are the whole plot factors; ID is the subplot unit, and TIME is the subplot factor. If 3 plants in each pool were randomly assigned at the beginning of the study to be destructively sampled at different TIMEs, then you do not need anything fancy for the covariance structure: I'd consider either CS or CSH.   With respect to PART: Do you want to compare metal concentrations among PARTs, to do separate analysis of each PART, to analyze the mean over PARTs, or something else?   But back to lack of replication. You need to sort that problem out first, to your satisfaction and to the satisfaction of anyone who will be evaluating your work (committee, reviewers, etc.) before turning your attention to your other analysis questions. You could look into the methodologies presented here https://www.amazon.com/Analysis-Messy-Data-Nonreplicated-Experiments/dp/0412063719 While searching for that link I noticed a symposium on the topic here https://dl.sciencesocieties.org/publications/cs/tocs/46/6#h1-ANALYSIS OF UNREPLICATED EXPERIMENTS (SYMPOSIUM) It may be that a descriptive approach would be best, no statistical inference tests.   ... View more

You should get a random effect estimate for each hospital.   There is not enough information in your post to allow any more sleuthing. The Community would need example data and your actual code (where the actual code using the example data reproduces the problem) to have any hope of sorting out what might be going wrong. ... View more

Yes, TRIAL is the effect of pre versus post. ... View more

Good for your critic. You should definitely question the correctness of the model when it reports zero denominator degrees of freedom, no matter how much you like the results. Generally zero den df means that your model is over-specified.   And, in fact, your model is overspecified: you have BLOCK in both MODEL and RANDOM statements, which is not correct--you are asking the model to estimate the same parameters twice which makes the model unhappy. Theoretically, if BLOCK is a random effects factor, BLOCK and all interactions involving BLOCK are random effects factors. Consequently those terms generally should not be in the MODEL statement.   If you have at least one observation in each combination of TREAT and CYCLETIME, then you could consider this model:   proc glimmix data=autostats; class block treat cycletime; model log_N2O = treat|cycletime; random block; *random block*treat; /* might be included for type=ar(1) */ repeated cycletime / subject=block*treat type=ar(1); lsmeans treat|cycletime; run; Note that "channel" in your model is (I think) equivalent to BLOCK*TREAT. You don't need to use CHANNEL--BLOCK*TREAT works just fine--but if you do, it should be in the CLASS statement.   If the TREAT x CYCLETIME factorial is incomplete and if TREAT*CYCLETIME is included in the treatment structure of the model, then various lsmeans will be reported as "non-est" (not estimable) and the interpretation of the interaction may be (probably is) suspect.   A fixed effects factor with 75 levels (like CYCLETIME) is very unwieldy in an ANOVA model. If it is significant, how do you sort out which means are different from which other means? The number of pairwise comparisons is 2,775 (the combination of 75 things taken 2 at a time). 2,775!  Consider the impact on power of controlling for family-wise Type I error among 2,775 comparisons using the Tukey method. Plus I can't imagine that you actually care about each of the 75 means. Plus the interaction is even more unwieldy.   So I suggest giving serious consideration to dealing with CYCLETIME in some other way that makes sense in the context of your data. You could, for example, compute weekly averages (if that was defensible in context) and continue with a mixed-model ANOVA approach. Another approach is a regression of the response on CYCLETIME, maybe using spline regression rather than linear or curvilinear regression if the linearity assumption is not met. A regression approach would also accommodate your missing data problem. These sorts of models are very complex and definitely should not be pursued naively. (I've added italics for emphasis. You really need to know what you are doing with these models.)   To use CYCLETIME as the predictor variable in regression, you would need to convert it from a text variable to a numeric variable.   A few resources related to a regression approach:   Chapters 7 and 8 in https://www.sas.com/store/books/categories/usage-and-reference/sas-for-mixed-models-second-edition/prodBK_59882_en.html   https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_glimmix_sect018.htm   http://blogs.sas.com/content/iml/2017/04/19/restricted-cubic-splines-sas.html   Good luck!     ... View more

So you have 15 "replicates", 3 in each of 5 blocks?   If you had balanced data, then the interaction of TREAT and CYCLETIME would have 3 x 75 = 225 means. How would you go about interpreting interaction in this scenario? Would it be more parsimonious to regress the response on CYCLETIME and assess whether the 3 regressions are parallel across CYCLETIME? ... View more