# glmm with proportion data and high overdispersion

I have data of time budget behaviors in form of relative frequencies (Nr specific behavior/nr of total behavior observed). The best would be to perform a multinomial analysis, but it seems too hard to interpret results for me. So I am going with GLMM (which is not simple but I try to!). I decided for a binomial distribution with the rate of foraging (for example, then I will use other behaviors as responses) as response (numerical variable) and other 4 factorial variables as fixed factors, Id as random. My first model is then like this

mod1<-glmer(rate.for~PERIOD+DAY+AGE+ZONA+(1|ID),
data=timeb,weights=totale.attivit_,family="binomial")


if I calculate overdispersion then I got 2547.6/720 =3.5 which is high, right?

So now..how do I proceed? I saw that I cannot use negative binomial or beta; I also saw to ad a random term for each observation: this point, which I do not fully understand, is not working in the model, with problems of convergence.

This is how my data look like

$ID.OBS : int NA 1947 1943 1945 1954 1959 63 64 1956 1960 ...$ FAMILY      : Factor w/ 12 levels "ALTE","ATOLIMPO",..: 1 1 1 1 1 9 9 9 9
$id : Factor w/ 67 levels "N","b",..: 54 58 51 57 25 17 19 26$ NSCAN          : int  3 3 3 3 3 4 4 4 4 4 ...
$DAYCONT : int 72 72 72 72 72 72 72 72 72 72 ...$ PERIOD        : Factor w/ 3 levels "A","B","C": 1 1 1 1 1 1 1 1 1 1 ...
$DAY : Factor w/ 3 levels "D","E","F": 1 1 1 1 1 1 1 1 1 1 ...$ SEX          : Factor w/ 2 levels "F","M": 2 2 2 2 2 2 1 1 2 2 ...
$AGE : Factor w/ 3 levels "0","1","2+": 3 3 3 3 2 2 2 2 3 2 ...$ STATUS         : Factor w/ 3 levels "DOMINANTE","GIOVANE",..: 3 3 3 1 2 2 2 2
$ZONA : Factor w/ 2 levels "ALTA","BASSA": 1 1 1 1 1 1 1 1 1 1 ...$ rate.for       : num  0.2 0.5 0.5 0.4 0 ...
$rate.play : num 0.6 0.5 0.5 0 0 0 0 0 0 1 ...$ rate.gree      : num  0 0 0 0 0 0 0 0 0 0 ...
$rate.groo : num 0 0 0 0 0 ...$ rate.fight     : num  0 0 0 0 0 0 0 0 0 0 ...
$rate.look : num 0 0 0 0.6 0 0 0 0 0 0 ...$ rate.l.burrow  : num  0.2 0 0 0 1 0 0 0 0 0 ...
$rate.move : num 0 0 0 0 0 0 0 0 0 0 ...$ rate.hay       : num  0 0 0 0 0 0 0 0 0 0 ...
$rate.scream : num 0 0 0 0 0 0 0 0 0 0 ...$ rate.dig       : num  0 0 0 0 0 0 0 0 0 0 ...
\$ rate.mark      : num  0 0 0 0 0 0 0 0 0 0


Actually my rate of foraging behavior (nr of foraging event/total behavior) appears like this in the plot

I also was thinking to use only the number of foraging event instead of rate. In this case foraging would be a counts and I could use Poisson distribution; anyway the overdispersion remain high.

Thanks to any help!