# [R-sig-ME] Fwd: Priors for and estimating heritability from an ordinal and a Poisson animal model

Helen Ward h.l.ward at qmul.ac.uk
Tue Sep 25 16:37:16 CEST 2012

```Hi everyone,

I have posted this before, but I thought I'd try one more time in the
hope that someone can help :) Sorry if you've read it twice.

Helen

....

Hello everybody,

I've just come back to some models I was working on a while ago and was
hoping someone could help me clear up a couple of issues. My goal is to
calculate the heritability of two independent traits: number of deformed
toes, and age of 1st reproduction.

Number of deformed toes is a data set of integers ranging from 0 to 6:
it looks most like a zero-inflated Poisson distribution.
Age of 1st reproduction is a data set of integers ranging from 0
upwards: it has a clear Poisson distribution.

I have built animal models for these traits in ASReml specifying that
both data sets are Poisson distributed. However, I cannot compare my
heritability estimates with those estimated for other Gaussian traits as
in a Poisson model in ASReml the residual variance is fixed at 1.

I am now trying to model these traits in MCMCglmm, deformed toes in an
ordinal model and age of 1st repro in a Poisson model.

At the moment for deformed toes I am using

prior2=list(R=list(V=1, fix=1), G=list(G1=list(V=1, nu=1,
alpha.mu=0,alpha.V=100)))

model1<-MCMCglmm(Toes~1,random=~animal,family="ordinal",pedigree=ped,data=data,prior=prior2,nitt=500000,thin=300,burnin=300000,verbose=FALSE,pl=TRUE)
then

posterior.heritability1<-model1\$VCV[,"animal"]/(model1\$VCV[,"animal"]+model1\$VCV[,"units"]+1)to

calculate heritabilty.

For age of 1st repro I am using

prior1.1<-list(G=list(G1=list(V=matrix(p.var/2),n=1)),
R=list(V=matrix(p.var/2),n=1))

model1.1<-MCMCglmm(Poisson1strepro~1,random=~animal,family=”poisson”,pedigree=ped,data=data,prior=prior1.1,nitt=100000,thin=75,burnin=25000,verbose=FALSE)

then

posterior.heritability1.1<-model1.1\$VCV[,"animal"]/(model1.1\$VCV[,"animal"]+model1.1\$VCV[,"units"])

to calculate heritability

Please can someone comment on whether they think these priors and
methods of estimating heritability are OK?

Please can someone also tell me whether the heritability estimate from
the ordinal model means the same thing as a heritability estimated from
a model in which the residual variance is not fixed?

Finally, I would like to add a random factor (Year of birth) to both
models. Please can someone suggest how I might alter the prior in the
ordinal toes model to do so?

Many (many) thanks,
Helen

```