[R-sig-ME] Predicted values in MCMCglmm family="threshold"

[Jarrod Hadfield]

Hi,

have

cp<-c(-Inf, 0, cp.est, Inf)

where cp.est are the estimated cutpoints (if there are any - with 2  
categories there are none).

Have linear predictor nu = xb or nu=xb+zu. If the former (and there  
are random effects) then have v the sum of the variance components  
associated with that term, and if the latter have v as the units  
variance associated with that term.

Have obs<-1:k where k is the number of categories (2+the number of  
estimated cutpoints) and the probability of falling into a category  
conditional on nu and v is:

pnorm(cp[obs+1], nu , sqrt(v)) ? pnorm(cp[obs], nu, sqrt(v))

for family=threshold, and

pnorm(cp[obs+1], nu , sqrt(v+1)) ? pnorm(cp[obs], nu, sqrt(v+1))

for ordinal.

For example,

cp.est<-1
cp<-c(-Inf, 0, cp.est, Inf)
k<-2+length(cp.est)
obs<-1:k
nu<--1
v<-2
pnorm(cp[obs+1], nu , sqrt(v))-pnorm(cp[obs], nu, sqrt(v))

Jarrod


Quoting Shamil Sadigov <shamil at gmail.com> on Fri, 21 Mar 2014 14:56:25 +0200:

> Hi Jarrod,
>
> I am using the new family="threshold" in MCMCglmm version 2.18 with a
> 5-variate ordered response. I would like to obtain the predicted responses
> for on the original ordinal scale, but I am not sure how to do so for
> either "ordinal" or the "threshold" family.
>
>  1. For family="threshold" the posterior predicted probabilities are :
>
>                 post.pred[, keep] <- pnorm(post.pred[, keep], 0,
> sqrt(postvar[, keep]))
>
> How can I classify these probabilities into the original ordinal scale?
>
>
> 2. I can see that for family="ordinal", cut points (CP) are used in
> predict.MCMCglmm():
>
>   for (i in 2:(dim(CP)[2] - 1)) {
>                   q <- q + (pnorm(CP[, i + 1] - post.pred[, keep],  0,
> sqrt(postvar[, keep] + 1)) - pnorm(CP[, i] - post.pred[, keep], 0,
> sqrt(postvar[, keep] + 1))) * (i - 1)
>                                         }
> Are the thresholds and the posterior predictive values (using type =
> "terms") on the linear (latent variable) scale?
>
> What would be the interpretation of the predicted values obtained from
> using type= "response" with family = "ordinal"? (All 5 ordinal responses
> are coded 1-3, and the predicted values from predict.MCMCglmm are real
> numbers between 0-6.)
>
> Regards,
> Shamil.
>
> 	[[alternative HTML version deleted]]
>
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>



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