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

[David Duffy]

On Fri, 2 Nov 2012, Samantha Patrick wrote:

> 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).
>
> 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?)

Yes.

> [polychoric r's compared to Pearson r's] 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.

The alternative is the full multivariate genetic (or even genetic time 
series model[1]), where you could see if the between-occasion correlations 
are genetic or environmental (the latter may include measurement error). 
This should run in MCMCglmm as an ordinal model.  You can test if the 
covariances have a simple structure as under a straight measurement error 
model.  If the between-occasion correlations average ~0.5 you should have 
OK power I think.

[1] eg 
http://www.tweelingenregister.org/nederlands/verslaggeving/NTR_publicaties/Boomsma_BG_1987.pdf

-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at 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