[R] Question on overdispersion

[cct663]

I have a few questions relating to overdispersion in a sex ratio data set
that I am working with (note that I already have an analysis with GLMMs for
fixed effects, this is just to estimate dispersion). The response variable
is binomial because nestlings can only be male or female. I have samples of
1-5 nestlings from each nest (individuals within a nest are not independent,
so the response variable is the ratio of sons to daughters) and some females
have multiple nests in the data set (so I need to include female identity as
a random effect). 

Here is an example of what the three vectors used in the model look like
(the real data set is much bigger, just to illustrate what I’m talking
about):

male_chick_no=c(2,4,1,0,3,5,2)
female_chick_no=c(1,0,3,3,1,0,2)
FemaleID=c(A,A,B,B,C,D,E)

My first question relates to coding the test in R. I received this suggested
R syntax from a reviewer:

SexRatio = cbind(male_chick_no, female_chick_no)

Model <- lmer(SexRatio ~ 1 +(1|FemaleID), family = quasibinomial)

But when I try to use this in R I get the error: “Error in glmer(formula =
ratio ~ 1 + (1 | femid), family = quasibinomial) : "quasi" families cannot
be used in glmer”.

I’ve tried playing around with some other mixed model functions but can’t
seem to find one that will provide an estimate of dispersion and allow me to
include my random effect. 

Is there some other function I should be using? Or is there a different
syntax that I should use for lmer?

My second question is more general: I understand that with binomial data
overdispersion suggests that the observed data have a greater variance than
expected given binomial errors (in my case this means that more nests would
be all male/all female than expected if sex is random). So with binomial
errors the expected estimate of dispersion is 1, if I find that dispersion
is > 1 it suggests that my data are overdispersed. My question is, how much
greater than 1 should that number be to conclude that the data are
overdispersed? Is there a rule of thumb or does it just depend on the
dataset? 

I was thinking of doing a randomization test with the same structure (nest
size and female id) as my real data set but with sex ratio of each nest
randomized with a 50:50 chance of individuals being sons or daughters and
comparing my observed dispersion to the distribution of dispersions from the
randomization test. Would this be a valid way to ask whether my data are
overdispersed? Is it even necessary?

Any help/advice that you can provide would be greatly appreciated. I am
relatively new to R so explicit instructions (i.e. easy to follow) would be
wonderful.

Thanks.

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