Yes, that data will work. The binomial distribution is a default for models that use the events/trials syntax, but it can be applied to aggregate values as well, see  example 51.4 Quasi-likelihood Estimation for Proportions with Unknown Distribution    https://documentation.sas.com/doc/en/statug/15.2/statug_glimmix_examples07.htm and the complete code: https://documentation.sas.com/doc/en/pgmsascdc/v_032/statug/statug_code_gmxex04.htm . One thing that you will want to do is put the extreme values of 0 and 1 back into the analysis dataset, rather than 0.005 and 0.995. The binomial distribution has support on the closed interval that includes zero and one when a logit link is used.   SteveDenham ... View more

@PaigeMiller , I really wish you could convince toxicologists and especially clinical pathologists about #4. I've spent the last 15 years trying to convince folks that taking the average of several animals' percent change from baseline doesn't result in a number that applies to the population the way they think it does..   SteveDenham. ... View more

Well, it could be that using a beta distribution with the default log link is the problem.  This phrase: Persons are  (attempted to be) assessed by a single yes/no item. indicates to me that a binary/binomial distribution with a logit link may be more appropriate. In each case, the response variable is the proportion of Yeses out of the number of occasions for observing either Yes or No, rather than a proportion defined by a continuous variable divided by a larger, different continuous variable.  With that in mind, take a look at Stroup and Claassen's paper:  https://econpapers.repec.org/article/sprjagbes/v_3a25_3ay_3a2020_3ai_3a4_3ad_3a10.1007_5fs13253-020-00402-6.htm . The full paper may be behind a paywall (Springer) but keep digging and you'll find a pdf copy.   So the pseudo-likelihood method they used was the default for GLIMMIX - RSPL.   Good luck.   SteveDenham ... View more

I am going to follow this closely as this is an interesting question that I don't have an answer for.  Some additional information could be helpful, such as what are the numerator and denominator in the calculation of compliance2, how many records you have, and whether you have tried a pseudo-likelihood approach, rather than the quadrature.   SteveDenham. ... View more

I know that the design looks like year and site are random effects, but there really are not enough levels for this analysis with the number of records you have.  Consider making year and trial site fixed effects, and along with all the other stuff I threw out there, see if that alleviates the problem of not being able to get initial estimates to yield a valid objective function.  If it works, then you can use the solution to cobble together initial values that may work for the model with full random effects.   The other thing that occurs to me is that you may have a lot of empty (or nearly empty) cells. This is another cause of the failure to find initial estimates that yield a valid objective function. Look at a PROC FREQ or PROC MEANS output for each of your combinations of random effects. Since nested components are handled the same as crossed components in the Z matrix, this might give you a better feel for the arrangement of data.   SteveDenham ... View more

The key in the log isn't necessarily the ERROR statement, but the WARNING immediately following. If you can't get started from the initial values, then the default QUANEW optimization will never converge. The model you have specified has trt as a continuous variable, so even if it converged you wouldn't have anything for the LSMEANS statement.   Something you might consider given this is to add trt to the CLASS statement. Next, how many years worth of data do you have?  How many trials within each year?  If the N for these aren't large enough to provide stable estimates, you will probably have at least some sort of convergence difficulty. The next thing to consider is that the lognormal distribution might not be the best to choose from a convergence standpoint.  Have you tried a gamma or exponential distribution with a log link? These will approximate a lognormal and may be more likely to converge.  Finally, can you rewrite your RANDOM statements to use the /subject= syntax?  That will also improve the odds of convergence.  If all of these lead back to the same issue, then there are other possibilities involving the PARMS statement or some options for the PROC GLIMMIX statement.   SteveDenham ... View more

I doubt that the point at the top right is an outlier, but I would say that it is a very high influence/leverage point that will have a big influence on the fit/correlation and the estimates of the slope and intercept.  Be sure you know the difference.  If I had to pick a potential outlier, it would be the point at about temp=82, chirps ~ 150.  But the point here is that the appropriateness of a linear model is better determined by the shape of the QQ plot, and the location of the high leverage point.   Consider a plot where many points are down in the lower left-hand corner and a single point is in the upper right-hand corner.  If you fit a regression line to data like that, it is likely to be linear with a large R squared value, all due to a single point. So, in your case, if the Cook's D value for that extreme temperature/chirp number observation is greater than an F value with 1 and 14 df and a probability of 0.5.= 0.479, then it is probably distorting the fit to be "more linear". I wish you had been provided the DFFITS value and the studentized residual value in addition to Cook's D..   That still doesn't answer the question of whether a linear model is appropriate.  I would say that it is appropriate if that high point is biologically plausible, but may not be appropriate (can't tell without the data) if that point is removed from the analysis.   SteveDenham ... View more

I would not expect GLIMMIX to do a good job with censored data, as the missing values are not at random.  However, with complete data the BYOBS method for joint distributions that @StatDave brought up is a good idea. The procs FMM and HPFMM allow for truncated normal and Poisson distributions. Censored data can be done with PHREG as you mention, but tobit models (PROC QLIM or ENTROPY in SAS/ETS, LIFEREG in SAS/STAT) may provide better estimates (stress on the word MAY).   SteveDenham ... View more

The link gives an R approach to answering the question using a likelihood ratio test: https://www.statology.org/negative-binomial-vs-poisson/  To accomplish the same thing in SAS, use the converged log likelihood value from the two choices. The difference should be distributed as a chi-squared variate with a single degree of freedom.  But the big thing that is in this website is "LOOK AT THE RESIDUALS GRAPHICALLY".  Over or underdispersion to the degree that inferences may be affected should be readily apparent from a plot of residuals vs. predicted values.   SteveDenham ... View more

Well, that would have been good to know earlier.  If you have homogeneity of variance across the time points, you can use PROC GEE or PROC GLIMMIX for the analysis.  If the variances are heterogeneous across time then GLIMMIX allows for the fitting of heterogeneous variance using a heterogeneous compound symmetry variance-covariance matrix or an unstructured covariance matrix. The following assumes heterogeneity by time.   proc glimmix data=yourdata plots=all; class time subjectid; model force = time; random time/subject=subjectid type=csh residual; lsmeans time/diff cl; run; This fits a model where the residuals are heterogeneous but normally distributed.  The plots will enable you to make a decision on whether this is a reasonable assumption.  The lsmeans statement will yield comparisons between all 10 timepoints. Note that this will involve 45 comparisons which are likely to not be independent.  Control for multiplicity can be added to the lsmeans statement.  For GLIMMIX, the adjust=simulate (seed=<pick a number>) usually provides the best control of Type I error, especially when combined with the stepdown option.     Since this is fitting an R-side variance-covariance matrix with no random effects, it could also be fit using PROC GEE. I will leave this for @StatDave to suggest some starting code.   SteveDenham   ... View more

Here is a snippet from our protocols regarding analysis of cytokine data:   For cytokines, a repeated measures analysis (mixed model) will be conducted. For each endpoint, the model will test for the effects of treatment, time, and the interaction of treatment and time(1). A lognormal distribution will be assumed unless there are several values outside the range of quantitation, in which case a rank transformation will be applied. Ranks will be calculated across all timepoints, and the analysis will use the ANOVAF option and MIVQUE0 technique in SAS PROC MIXED(2) .   (1)Littell RC, Milliken GA, Stroup WW, Wolfinger RD. SAS System for Mixed Models. Cary (NC): SAS Institute Inc.; 1996. (2)Brunner, E., Domhof, S., and Langer, F. Nonparametric Analysis of Longitudinal Data in Factorial Experiments, New York: John Wiley & Sons.; 2002.   We use PROC GLIMMIX, but you could get essentially the same analysis using PROC MIXED if you log transformed the data before analysis.  The code we use  is estimating the marginal effects, as there is only an R-side variance-covariance matrix being estimated.  Given that, PROC GEE or PROC GENMOD are also candidates. My gut feeling is that you would log transform the data before analysis rather than using a LOG link function, but I will defer to @StatDave for a better response than "a gut feeling".   SteveDenham ... View more