trouble getting data scale predictions from a binomial MCMCglmm model

Hi Jarrod and thanks for a quick reply.

But the example I gave does not have random effects so the sum of
variance components is 1 as used in my calculation:

summary(m2c.3$VCV)

Iterations = 3001:12991
Thinning interval = 10
Number of chains = 1
Sample size per chain = 1000

1. Empirical mean and standard deviation for each variable,
  plus standard error of the mean:

         Mean             SD       Naive SE Time-series SE
            1              0              0              0

2. Quantiles for each variable:

2.5%   25%   50%   75% 97.5%
   1     1     1     1     1

And with marginal=NULL the predictions are the same as without it in
this case. So, I am still not sure I got it. The predict.MCMCglmm  
seems
to do something differently than my direct model matrix & coefficients
approach in the example below.

regards, Kari

On Wed, 2011-03-23 at 12:48 +0000, Jarrod Hadfield wrote:

Dear Kari,

The default in the predict function is to obtain the expectation  
after
marginalising the random effects, hence you should be multiplying c2
by the sum of the variance components (if the random structure is a
simple grouping) if you want to obtain the same answer.  
Alternatively,
you could specify marginal=NULL in the call to predict and this  
should
be the same as your preds.data.

See the posts for https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q1/005575.html
 also.

Cheers,

Jarrod



On 23 Mar 2011, at 12:19, Kari Ruohonen wrote:

Hi,
I have fitted a binomial model (logit link) with MCMCglmm by fixing
the
unit variance to 1 as discussed in the CourseNotes of MCMCglmm.

Now, I would like to get predictions on the data scale. I know there
is
a predict function that does this but I need to be able to predict
outside R. With the usual X%*%b where X is the model matrix and b  
the
vector of coefficients I get predictions on the link scale. The
predictions I get match those from the predict.MCMCglmm method with
the
type="terms" option. However, I cannot figure out how to get the
predictions on the data scale. CourseNotes discuss and give an  
example
of scaling the coefficients suitably with c2 <- (16*sqrt(3)/ 
(15*pi))^2
and then dividing with (sqrt(1+c2*residual var)) to obtain estimates
under residual variance =0 but I cannot figure out how to apply this
to
the case of predictions.

Here is a small example based on one in the CourseNotes:

treatment<-gl(2,25)
y<-rbinom(50,1,c(.5,.001)[treatment])
data.bin<-data.frame(treatment=treatment,y=y)
prior.m2c.3<-list(R=list(V=1,fix=1),G=list(G1=list(V=1,nu=.002)))
m2c.3<-
MCMCglmm
(y~treatment,data=data.bin,family="categorical",prior=prior.m2c.
3,verbose=FALSE)

# the next predictions correspond to those from predict.MCMCglmm
with "
# type="terms"
preds.link<-m2c.3$X%*%summary(m2c.3$Sol)$statistics[,1]

# but these do not correspond those with type="response"
preds.data<-plogis(preds.link[,1]/sqrt(1+c2*1))

I am obviously missing something and would be grateful to someone
helping me out.

Many thanks, Kari