Predicted values in MCMCglmm family="threshold"

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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.

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Hi,

? should be - (and microsoft should be *)

Jarrod

Quoting Jarrod Hadfield <j.hadfield at ed.ac.uk> on Fri, 21 Mar 2014  
14:14:50 +0000:
Hi,

have

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