[R-sig-ME] MCMCglmm ordinal: clarification on estimating an intercepts only model and interpreting cutpoints

[Jarrod Hadfield]

Hi,

The polr and MCMCglmm models you have fitted are equivalent.  If you  
have a look at (m2$CP-m2$Sol)/sqrt(2) you will find them to be  
identical to the cutpoints estimates from polr. The sqrt(2) comes from  
the fact that there is the probit variance and the `residual' variance  
as specified in the R element of the prior.

The probability of observing an outcome in category k is

pnorm(eta, CP[k-1], 1)-pnorm(est, CP[k], 1)

where in your case the latent variable eta is Gaussian with mean equal  
to the Intercept estimate and a variance of 1.  One cutpoint is not  
identifiable from the intercept so CP[1] is set to zero. Therefore  
-m2$Sol/sqrt(2) is equal to the first cutpoint in polr.

Cheers,

Jarrod





Quoting Jonathan Salerno <jdsalerno at ucdavis.edu> on Wed, 13 Mar 2013  
18:14:30 -0700:

> I posted a confusing version of this question a few weeks ago, so here's an
> attempt at clarifying:
>
> In short, I'm trying to replicate an intercept-only (ie, no predictors)
> model output of polr() using MCMCglmm as an initial step before building up
> a more complex model family that includes varying intercept and slope
> effects (ie, random, clustering, multi-level effects) and multiple
> predictors.
>
> To estimate the intercepts of an ordinal model with no predictors, lets say
> it's specified as follows in polr():
>
> m1 <- polr( as.ordered(h) ~ 1, data=d1, Hess=T, method="probit"),
>
> where h is a 7 category response for household hunger.  Before building in
> predictors, I wish to compare the cumulative link estimation of intercepts.
>  My question is whether the following specification in MCMCglmm will
> approximate the above polr fit:
>
> prior <- list(R=list(V=1, fix=1))
> m2 <- MCMCglmm( as.ordered(h)
> ~ 1, family="ordinal", pl=F, pr=F, data=d1,prior=prior).
>
> The second part of this question regards how to interpret the MCMCglmm
> cutpoints in terms of intercepts.  I've read the few posts from you and Ben
> Bolker answering similar questions, but I'm not following the process.
>  Specifically, I don't understand which value of a latent variable used in
> the cumulative probability distribution function is used to compute the k-1
> intercepts from the cutpoint outputs of MCMCglmm.
>
> Apologies for my difficulty, but your help is much appreciated.  Thanks
> very much, and good day.
>
> jon
>
> 	[[alternative HTML version deleted]]
>
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