r - Fit a polynomial glmer (lme4) model - Cross Validated

having dim memories of subject uni, i'm struggling bit fitting polynomial binomial mixed effects model 2 nested random effects.

my data counts of success , failures (s , f) @ variety of values of x. there 2 random effects, r1 , nested random effect r2.

i try fitting polynomial model, ninth order , use aic values find minimum adequate model, i'm unsure of syntax.

so i've got 3 questions really:

is code below correct?

what syntax fit glmer polynomial?

is whole thing statistical nonsense, , should try different approach?

thanks help, code below:

require(lme4)  ## sample set: ## x fixed effect ## s count success ## f count fail ## r1 random effect 1 ## r2 random effect 2  sample.set <- data.frame(x = runif(1000,-100,100),                          s = round(runif(1000,100,1000),0),                          f = round(runif(1000,100,10000),0),                          r1 = c(rep("a",250), rep("b",250), rep("c",250), rep("d",250)))  sample.set$r2 <- sapply(sample.set$r1,function(x){if(x == "a")                {as.character(round(runif(1,1,5), 0 ))} else                                                   if(x == "b") {as.character(round(runif(1,6,10), 0))} else                                                   if(x == "c") {as.character(round(runif(1,11,15),0))} else                                                                {as.character(round(runif(1,16,20),0))}})  prop.tab <- cbind(sample.set$s,sample.set$f)  mm.model <- glmer(prop.tab ~ sample.set$x + (sample.set$x | sample.set$r1) + (sample.set$x | sample.set$r2),                   family = binomial, control = glmercontrol(optimizer = "bobyqa"), nagq = 0)