Hi David

Thanks again for your reply - it has helped a lot.  Specific questions 
addressed below:
>
>     -----Original Message-----
>     From: David Duffy <David.Duffy@qimr.edu.au>
>     To: Samantha Patrick <spatrick@cebc.cnrs.fr>
>     Date: Thu, 1 Nov 2012 16:02:35 +1000
>     Subject: Re: [R-sig-ME] Heritability of ordinal data in MCMCglmm
>     and estimatingfixed effects
>
>     On Wed, 31 Oct 2012, Samantha Patrick wrote:
>
>     >> 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.
>
>     Yes, but if your model is that there is a single underlying trait
>     that is
>     being measured with error, then Va/(Va+Ve) estimates the
>     heritability of
>     the trait, while Va/(Va+Ve+Vm) is attenuated.  The equivalent
>     analysis is
>     to analyse the average score across the occasions.  What is the
>     between
>     occasion correlation in score? Have you fitted an ordinary LMM to the
>     scores?
>

The pearson's correlations between observations ranges from 0.18 - 0.75, 
depending on the year of testing (average 0.48; one year has a very low
repeatability).  I have used LMM both to estimate the repeatability and 
the heritability.  I know that often once you have more than 4 ordinal 
groups,
there is support for using a Gaussian error structure.  The 
repeatability using an LMM is virtually identical to that using MCMCglmm
with an ordinal structure.  The residuals from the LMM are quasi normal, 
and I think it is easily arguable that this is a suitable model.
However, I want to present both models in the paper for various reasons 
hence my attempts to get the ordinal model running.

So the heritability estimates using LMM were run in ASReml and the 
results are largely similar.  Running the full model as previously 
described:

Trait1~ Colony , random =~animal + BYEAR + MOTHER + ID

The esimates for BYEAR (0.00 +/- 0.00) and MOTHER (0.00 +/- 0.00) are 
both zero, as we find when using MCMCglmm.   However, ASReml estimates:
  ID (Vpe) to be 0.35 +/ - 0.15 and animal (Va) to be 0.19+/-0.17, 
giving a heritability of 0.12.

Just to recap, MCMCglmm estimated:

And then extract the variance components and heritability as above:

animal = 0.00 (0.00-0.37); BYEAR = 0.00 (0.00-1.47) ; MOTHER=0.00 (0.00-0.25) ; ID=0.00 (0.00-1.45)

h^2  =0.00 (0.00-0.37)

>     Which comes to your measurement problem.  There are a few ways to fit
>     a measurement model for repeated ordinal data, usually involving
>     some kind
>     of factor analytic (or item response theory) model.  Most recently
>     we have
>     been using BUGs to fit an IRT model, and grabbing the latent
>     factor scores
>     (BLUPs) from that.
>     The psych library can estimate polychoric correlation matrices for
>     your
>     occasions, and fit a factor model, but I don't think you can force the
>     correlations to be equal.  There are numerous R IRT packages. eg
>     classify,
>     ltm, that could give you scores based on the repeated measures.
>
OK this is great - I will have a look into this.
>
>
>     WRT your full model (A + maternal (brood?) effects + occasion +
>     byear),
>     when I said it didn't work I meant that either maternal and additive
>     genetic effects are unable to be simultaneously estimated due to the
>     structure of your data, or that MCMCglmm had got stuck at a false
>     maximum.
>
Having thought a bit more about this, I have made a really stupid error: 
There is only one chick per year, so maternal effects are the same as Va!

>     Can you generate some summary statistics, such as
>     parent-offspring, sibling, half-sibling correlations for score
>     averaged
>     over measurements?  These could be polychoric correlations, or simply
>     Pearson correlations.
>

One of the reasons why I question whether using a Gaussian distribution 
(fitting a LMM) is correct is that the Mother- Offspring (M-O), father- 
offspring (F-O) and sib-sib (S-S)regressions all have
a Pearson's R2 <0.05.  Using polychoric correlations (I ran these in the 
polycor package but as I understand it will run the same test?), the 
results are very different:

M-O = 0.34
F-O = 0.40
S-S = 0.13

The conclusions seems to be that the best model to estimate heritability 
would be to fit the first observation per individual, such that:

Trait1~ Colony, random =~animal + BYEAR

and examine the models with and without BYEAR, fitted in MCMCglmm. I can then use repeated measures to
estimate the repeatabilities and extract the blups or single scores per individual using an IRT model.

Thanks for all your help and advice - it is very much appreciated!

Sam


>
>     Cheers, David Duffy.
>
>     --
>     | David Duffy (MBBS PhD)                                         ,-_|\
>     | email: davidD@qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /
>         *
>     | Epidemiology Unit, Queensland Institute of Medical Research  
>     \_,-._/
>     | 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v
>

-- 

Dr Samantha Patrick
Post Doctoral Fellow
Centre d'Etudes Biologiques de Chizé - CNRS
79360 Villiers-en-Bois
France
T:+33 5 49 09 78 46
M:+33 6 75 06 34 51
Skype: sammy_patrick
http://www.cebc.cnrs.fr/Fidentite/patrick/patrick.htm
http://www.researchgate.net/profile/Samantha_Patrick/


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