For a short illustration of using the MIXED procedure to do MANOVA, see   http://blogs.sas.com/content/sastraining/2011/02/02/the-punchline-manova-or-a-mixed-model/   The column compares GLM and MIXED, and also notes the use of a mixture of distributions in GLIMMIX like @SteveDenham suggested, which would be very handy if different traits followed different distributions.   Edit: You can certainly use GLIMMIX for data that follow a normal distribution. ... View more

Oops, my apologies. A sudden realization that I have the wrong vision here, and rather than edit my first response, I'll add another.   The amount of time spent under LED light is not independent of the amount of time spent under CFL light, and the response can be defined by only one or the other. But then the light factor is no longer needed, because we do not have response values under the two different light levels.   So, I would try using the proportion of total time spent under LED light as the response:     proc glimmix data=have method=laplace; class pen day; model proportionLED = / dist=beta intercept s; random pen day; estimate "Intercept" intercept 1 / ilink cl; run;   and I would test the hypothesis that proportionLED = 0.5 (in other words, whether half of the time is spent under LED light and thus half under CFL and thus no preference), which would be accomplished by testing whether the intercept = zero (because the beta distribution uses a logit link, and logit(0.5)=0). Placing a confidence interval on the intercept would be nicely informative. ... View more

Stacy, you might find this exchange interesting. @PGStats built a nice example.     https://communities.sas.com/t5/SAS-Statistical-Procedures/Should-I-use-quot-Offset-quot-or-add-a-quot-rate-quot-variable/td-p/324342   ... View more

Perhaps the best experimental design advice ever came from Ronald Crosier, who said on sci.stat.edu at least two decades ago: No one should ever do an experiment without analyzing it first. (See http://mathforum.org/kb/message.jspa?messageID=1515598 for his elaboration on what he meant).   There surely are many ways to approach the analysis of this study. I will put forth one that is relatively simple but does make assumptions about sources of variance that may or may not be appropriate, and it involves statistical design and analysis concepts with which you likely are not familiar (for examle, crossed random effects, non-normal distributions).   I assume that the total amount of time for each trial is the same; consequently, the sum of the amount of time in the LED cage and the amount of time in the CFL cage is the equal to the total time. These two metrics are not independent: if you told me how much time the group spent in the LED cage, I could tell you exactly how much time it spent in the CFL cage. Consequently, you can use time spent in, say, the LED cage as the response and completely ignore the time spent in the CFL cage. (You could also use the proportion of total time spent in the LED cage; however proportions can have challenging distributional properties--the beta distribution in a generalized linear mixed model might be appropriate for a proportion response--and you might have better success with timeLED, perhaps with a transformation. The choice depends on the actual data values, as well as your preference for response.)   I would think of pen and day as crossed random-effects factors; this assumes that pen and/or day contribute to the variance of the response but have no effect on the mean response--in other words, neither pen nor day are fixed effects factors--which seems plausible to me (but may not be a correct assumption). The intersection of pen (with 2 levels) and day (with 6 levels) is a unique group of 3 birds (I'm assuming that you have 12 different groups of birds), and the experimental unit defined by this intersection==group_of_birds (which may also be ==trial) is the experimental unit for the fixed-effects factor, light. These assumptions lead us to    class pen day light; model timeLED = light; random pen day;   Issues that might arise: (1) timeLED may not be normally distributed with homogeneous variances for both light levels; (2) variance among pens and/or among days may have estimation problems; I would expect both variances to be small (but, again, that might not be a correct assumption).   An excellent resource is https://www.sas.com/store/books/categories/usage-and-reference/sas-for-mixed-models-second-edition/prodBK_59882_en.html. Time spent with this text is not time wasted.    I hope this helps get you going.   ... View more

Theoretically, density data cannot follow a negative binomial distribution because density data do not take integer values.   Unlike (at least some) packages in R, the GLIMMIX procedure accepts non-integer data in conjunction with the negative binomial distribution and appears to deliver valid results.    That said, my preference for modeling density based on counts is to use an offset (which is the third model in the code below). This approach is particularly advantageous if, say, plot areas are variable.   dpost: post-treatment density dpre: pre-treatment density npost: post-treatment count npre: pre-treatment count _log: log transformation   title1 "Using density with negative binomial distribution"; proc glimmix data=have method=laplace; nloptions tech=nrridg; class trt; model dpost = dpre_log trt dpre_log*trt / dist=negbin; lsmeans trt / ilink; output out=glmm_out pred=pred student=student; run; proc sgplot data=glmm_out; loess x=dpre_log y=student; refline 0 / axis=y; run; title1 "Using count with negative binomial distribution"; proc glimmix data=have method=laplace; nloptions tech=nrridg; class trt; model npost = npre_log trt npre_log*trt / dist=negbin; lsmeans trt / ilink; output out=glmm_out pred=pred student=student; run; proc sgplot data=glmm_out; loess x=npre_log y=student; refline 0 / axis=y; run; title1 "Using count with negative binomial distribution with offset to obtain density"; proc glimmix data=have method=laplace; nloptions tech=nrridg; class trt; model npost = npre_log trt npre_log*trt / dist=negbin offset=area_log; lsmeans trt / ilink; output out=glmm_out pred=pred student=student; run; proc sgplot data=glmm_out; loess x=npre_log y=student; refline 0 / axis=y; run;     ... View more

I'll ask, because it's a not-uncommon misconception: Are you checking normality using the observed data combined over treatment groups or using the residuals from a model? The former approach is bad, the latter approach is good. Distributional assumptions are conditional on the predictor variables.   Something of an aside: If the number of trees is "big enough", the Poisson distribution can be approximated by a normal distribution. Even if the data within each treatment group are normally distributed, the treatment groups could have different variances. Unequal variances might be accommodated with a log transformation or a heterogeneous variances model, as well as other approaches. So a model invoking a normal distribution might work, or it might not, depending on the data. If the counts are substantially overdispersed, then a model based on normal distributions might be less likely to be satisfactory. ... View more

Stepping back a bit: Is "tree density" a count (i.e., does "tree density" take integer values)? Typically, density is a rate: count/area. Is area the same for all experimental/observational units? I'm pondering here whether the negative binomial distribution is your best choice.    If tree density is a count (and now for clarity, I'll refer to "tree density" as "tree count"), then a negative binomial distribution might be appropriate. The canonical link for the negative binomial distribution is the log. Unless you invoke a curvilinear (e.g., quadratic) model, the relationship between the response and the covariate is assumed to be linear in the GLIMMIX procedure (generalized linear mixed model), which roughly translates into a linear relationship between log(post-tree-count) and the covariate (noting of course, that a log transformation of post-tree-count is not the same as a log link). Logically, I then would consider a log transformation of pre-tree-count. Plot log(post-tree-count) against log(pre-tree-count) and visually assess the relationship. Does it look linear? You can color- or symbol-code points by other predictor variable values as well for (potentially) additional insight.   ... View more

A different coding system will not "make the sample fit the population." You really ought to look into SURVEYLOGISTIC, it might be just the right tool for your problem, and it is able to make the weighted predictions that you appear to be interested in. ... View more

I recommend that you look into the SURVEYLOGISTIC procedure to deal with unequal weights. Search   lexjansen.com  for useful papers on SURVEYLOGISTIC and read the SURVEYLOGISTIC documentation to see whether this procedure would be appropriate for your study.   If you have data in hand, which appears to be the casee, then the methods by which those data were acquired, the definitions of variables, etc. are already determined, and you would be able to share those if you chose. ... View more