[R-sig-ME] MCMCglmm binary data

[Jarrod Hadfield]

Hi,

If you want to fit a probit model I would use family="threshold". It 
omits the additional overdispersion term and so you can simply calculate 
the link-scale h2 as Va/(Va+1) if you fixed the residual variance to 
one. This is the 'standard' probit model. For family="ordinal"  the 
link-scale h2 is Va/(Va+1+1) if you fixed the residual variance to one. 
Additionally, using family="threshold" mixes better. In both cases there 
is now the option (v2.25 and above) to specify trunc=TRUE in the call to 
MCMCglmm. This stops the latent variable going in to extreme probability 
regions resulting in numerical errors which can be an issue with binary 
models.

Cheers,

Jarrod


On 11/10/2017 22:04, Pierre de Villemereuil wrote:
> Hi,
>
>> I am running an 'animal model' for a binary trait (0 or 1 value) using
>> MCMCglmm. After reading Hadfield's course notes, i fixed the residual
>> variance to 1 and used an inverse gamma distribution for the additive
>> variance in my prior, and chose the family as "categorical" (link =
>> logit)  since there is no order here. h2 would equal Va/Va+1+π²/3, right?
> It depends on which kind of scale you wish to compute h². Here you get an estimate that can be related to a "threshold model". It might be sensible or not, depending on your biological question. You can also get an estimate on the data scale through the QGglmm package. You might want to have a read at the following:
> http://www.genetics.org/content/204/3/1281
>
> Also, I would recommend using "ordinal" rather than "categorical", as the probit link bears connection with the classical threshold model and might make more biological sense. There is no question of ordering for binary data (as it is a "degenerate" case in that regard). You might have specific reasons for using "categorical" of course.
>
>> Also, a different study was suggesting to use a χ² distribution (V=1,
>> nu=1000, alpha.mu=0, alpha.V=1) as the prior distribution for binary
>> traits (and only binary traits) when the sample is big enough (in my
>> case N = ~5000). I wanted to know your opinion on this and if I should
>> opt for it.
> Yes, this prior has usually better properties for binary data. It resulted in a much better precision and better accuracy in simulations. See Appendix B of the following (sorry for the auto-promotion...):
> http://onlinelibrary.wiley.com/doi/10.1111/2041-210X.12011/full
>
> Hope this helps,
> Pierre.
>
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