Hi R-helps,

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).

 Fish ID Group ID Diet quality Babies for paternity Success Failure
Proportion  1 High 1 9 5 4 0.556  12 High 1 7 5 2 0.714  15 High 1 7 4 3
0.571  20 High 1 6 5 1 0.833  32 High 1 7 2 5 0.286  37 High 1 3 1 2 0.333
48 High 1 4 1 3 0.25  53 High 1 10 0 10 0  65 High 1 3 3 0 1  70 High 1 4 4
0 1  77 High 1 7 2 5 0.286  82 High 1 6 6 0 1  96 High 1 8 2 6 0.25  104
High 1 12 10 2 0.833  111 High 1 4 3 1 0.75  123 High 1 6 5 1 0.833  128
High 1 8 8 0 1  133 High 1 6 5 1 0.833  144 High 1 12 6 6 0.5  152 High 1 13
11 2 0.846  159 High 1 8 1 7 0.125  164 High 1 4 1 3 0.25  169 High 1 6 2 4
0.333  5 Zero 0 9 4 5 0.444  10 Zero 0 7 2 5 0.286  17 Zero 0 7 3 4 0.429
22 Zero 0 6 1 5 0.167  36 Zero 0 7 5 2 0.714  39 Zero 0 3 2 1 0.667  44 Zero
0 4 3 1 0.75  51 Zero 0 10 10 0 1  63 Zero 0 3 0 3 0  68 Zero 0 4 0 4 0  73
Zero 0 7 5 2 0.714  84 Zero 0 6 0 6 0  94 Zero 0 8 6 2 0.75  106 Zero 0 12 2
10 0.167  109 Zero 0 4 1 3 0.25  121 Zero 0 6 1 5 0.167  132 Zero 0 8 0 8 0
137 Zero 0 6 1 5 0.167  142 Zero 0 12 6 6 0.5  154 Zero 0 13 2 11 0.154  157
Zero 0 8 7 1 0.875  168 Zero 0 4 3 1 0.75  173 Zero 0 6 4 2 0.667

I ran the following codes to have my results:

###Proportion estimate:
p<-Data$Success/(Data$Success+Data$Failure)
plot(Data$Group.ID,p,ylab="Proportion of success")

###Response variable:
y<-cbind(Data$Success,Data$Failure)
model1 <- glm(y~Diet.quality, data=Data, family=binomial)
summary(model1)
plot(model1)# gives Q-Q plots
###The residual deviance is 152.66  on 44 d.f. so the model is quite badly
overdispersed:
#152.66/44 where The overdispersion factor is almost 3.46 (unbelievable).

## model with logit link functions and weights:
model2<-glm(cbind(Success,Failure)~Group.ID,data=Data,
family="binomial"(link="logit"),weights=Success+Failure)
summary(model2)
###The residual deviance is 1196.1  on 46 d.f. so the model is quite badly
overdispersed:
#1192.1/44 where The overdispersion factor is almost 27.09 (unbelievable).

#The simplest way to take this into account is to use what is called an
#‘empirical scale parameter’ to reflect the fact that the errors are not
#binomial as we assumed, but were larger than this (overdispersed) by a
factor of 3.38.

model3<-glm(y ~ Group.ID,data=Data,family="quasibinomial")
summary(model3)

###Note that the ratio of the residual deviance and the degrees of freedom
is still
#larger than 1, but that is no longer a problem as we now allow for
overdispersion.


Each models gives me different results with overdispersion. So, can any one
help me to give me some valuable suggesions to solve this problem. I'll
really appreciate your kind assistance and will grateful to you forever.

With kind regards,

Moshi
mrahmankufmrt@gmail.com

-- 
MD. MOSHIUR RAHMAN
PhD Candidate
School of Animal Biology/Zoology (M092)
University of Western Australia
35 Stirling Hwy, Crawley, WA, 6009
Australia.
Mob.: 061-425205507

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