What is the best way to model nested binomial data?

I have results from a simple experiment where organisms on a plate are exposed to one of 4 concentrations and the lowest concentration is the control. I have coded the concentrations as a factor. There are 25 organisms on a plate and the number that died is counted. The organisms are nested on a plate but if I analyze the proportion that died these become the observations. I have six plates at a concentration for a total of 24 plates. My main interest is overdispersion overall and perhaps at each level.
data.frame': 24 obs. of 7 variables: $Plate : num 1 2 3 4 5 6 1 2 3 4 ...$ Concentration: num 0.01 0.01 0.01 0.01 0.01 0.01 0.0208 0.0208... $Surviving : num 19 24 24 25 25 25 19 21 21 16 ...$ Prop.Surv : num 0.76 0.96 0.96 1 1 1 0.76 0.84 0.84 0.64 ... $Conc : Factor w/ 4 levels "0.01","0.0208",..: 1 1 1 1 1 1 2 2 ...$ Died : num 6 1 1 0 0 0 6 4 4 9 ... $Prop.Died : num 0.24 0.04 0.04 0 0 0 0.24 0.16 0.16 0.36 ... It seems that I only have residual error so I used glm. I get a dispersion estimate of 2.4 from M1<-glm(cbind(Died,Surviving)~Conc ,family = binomial, data=dfTest ) disperseM1<- sum(resid(M1,type="pearson")^2)/M1$df.residual

The quasibinomial family also yields a dispersion estimate of 2.4. The book I have on Mixed models advocates analyzing the raw data, not the proportions when one has 0 event proportions to assure that the random effects estimates do not mask the overdispersion.

1. If I just use the proportions do I still need a mixed effect? Should I use a Bernoulli link with the organisms nested within plates? SAS provides options for this. My book on mixed models advises this but it doesn't seem possible with glmer.
2. Is there any way to assess if the dispersion is equal at all concentrations? Is this of interest in a glmm model, the way equal vartance of groups is for ANOVA?
3. If I bootstrap the proportions, is this a good method to yield a 5pctile and 95pctile for the dispersion parameter?
• Welcome to our site, Georgette! – whuber Oct 27 '17 at 13:56