[R-sig-ME] Paternity data analysis problem

[David Duffy]

On Wed, 24 Jul 2013, Moshiur Rahman wrote:

> I did an experiment with FAs ['High' and 'Zero'(no w-3) quality; n=24 for
> each group]. Then I did AI to see their sperm competitiveness based on
> their paternity performance. My data is as below where Fish ID- Blind ID
> for each fish; Group ID- Dietary group ID; Diet quality - High=1, zero=0;
> Babies for paternity- total no. of babies got from females; Success -
> Babies shared/paterned by focal male; Failure - Babies shared/paterned by
> competitor, Proportion - Success/(Success+Failure).
[...] 
> Each models gives me different results with overdispersion. So, can anyone
> help me to give me some valuable suggesions to solve this problem. I'll
> really appreciate your kind assistance and will be grateful to you forever.

For binomial data of this type, the simplest test of overdispersion
is a chi-square eg

chisq.test(x[x$Diet == 1, c("Success", "Failure")])

The quasibinomial model you fitted is one approach. It is
computationally easy, but may or may not capture the actual
differences between individual fish.  Another way is fitting
a gaussian-binomial GLMM (see http://glmm.wikidot.com/):

library(lme4)
glmer(cbind(Success, Failure) ~ Group.ID + (1|Fish.ID), data=x,
family=binomial(), nAGQ=20)

As usual, I would suggest reading around the area and speaking to a
local statistical expert about choosing the right model for your
exact problem (you may want to model the competition).

Cheers, David Duffy.