[R-sig-ME] Heritability of ordinal data in MCMCglmm and estimatingfixed effects

Samantha Patrick spatrick at cebc.cnrs.fr
Wed Oct 31 10:36:01 CET 2012

Hi David

Le 31/10/2012 05:49, David Duffy a écrit :
> On Tue, 30 Oct 2012, Samantha Patrick wrote:
>> Hi
>> I am estimating the heritability of an ordinal trait using MCMCglmm and
>> have come across two problems: one regarding heritability and one
>> specific to ordinal data sets.
>> _My data_
>> Trait1 = ordinal score from 0 - 4
>> Colony = factor with 2 options
>> ID = repeated measures per individual (818 individuals)
>> So the heritability:
>> /posterior.heritability1.1 <- model2.1$VCV[, "animal"]/(model2.1$VCV[,
>> "animal"]+ model2.1$VCV[, "ID"] + model2.1$VCV[, "units"]+1)/
>> /posterior.mode(posterior.heritability1.1)/
>> /h^2 = 0.21 (0.05- 0.45)/
> Why are there repeated measures?  Is the between-occasion variation of
> interest, or a nuisance?  That is, is animal/(animal+units) a better 
> measure of h2?

 >> There are between 1-4 measures of Trait 1 per individual.  I have 
run the model using only the first measure per individual  (as in h2 = 
animal/(animal+units)).  It has little effect on the heritability.  I 
have kept in the repeated measures as they allow as to calculate 
consistent environmentally induced differences ( see 
http://www.wildanimalmodels.org/tiki-index.php?page=repeated%20measures), and 
as I understand, it is better to use the full data set and control for 
any non independence.
>> /model2.2<-MCMCglmm(Trait1~ Colony , random =~animal + BYEAR + MOTHER +
>> ID, pedigree = Ped3, data = Data, prior = prior2.1,
>> family='ordinal',burnin = 20000, nitt = 500000, thin = 200, pr=TRUE)/
> doesn't work.

 >>> In what way? Sorry I don't quite understand this...
> How many levels of BYEAR, how many obs per year, do you want a random 
> regression on BYEAR (ie do you expect a linear relationship?)

 >>> BYEAR is a factor with 27 levels; a quick summary observations per 
0-5 obs = 3 levels
5-10 obs = 2 levels
20-50 obs = 10 levels
50-85 obs = 12 levels

There is no reason to suppose it would be a linear relationship; instead 
it is likely to represent cohort effects as a result of similarities 
between birds born in the same year so I have not tried to fit it as a 
random regression.

>> My second question is specific to ordinal analyses
>> I need to extract one score per individual and I wondered if
>> anyone knows if there is any methods for doing this? I can fit ID as a
>> random effect but I am not sure this changes anything, and is associated
>> with the curse of BLUPS.
> BLUPs are what you want, curse them ;)
 >>> The problem is for Gaussian data, Individual would be fitted as a 
fixed effect in the model, such that in its simplest form the model 
would be:

Trait1~ Colony + ID

and then the parameter estimates are extracted for ID and these are used 
as the individual measures.  This does not involve taking residuals from 
the model so seems to be statistically more sound than using BLUPs.  
While the two are normally highly correlated, there are differences and 
it seems unwise to go back to a method that has received much criticism.

Many thanks for your comments



Dr Samantha Patrick
Post Doctoral Fellow
Centre d'Etudes Biologiques de Chizé - CNRS
79360 Villiers-en-Bois
T:+33 5 49 09 78 46
M:+33 6 75 06 34 51
Skype: sammy_patrick

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