MCMCglmm error-in-variables (total least squares) model?

Hi,

The least parsimonious model (and not the one I would necessarily  
recommend fitting) is:

m1<-MCMCglmm(cbind(X1,X2,X3,Y)~trait,
              random=~us(trait):species+us(trait):species.ide,
              rcov=~us(trait):units,
              ginverse=list(species=tree))

where species and species.ide are columns of species names.

This deals with the measurement error on the species means, and also  
allows you to address the fact that the regressions of the X's on Y  
may be different at different levels. The method advocated by van de  
Pol has the problem that the mean in the mean centering is just the  
observed mean rather than the true unobserved mean. For example,  
imagine that you only had one observation for some of the species.   
You can obtain the regression coefficients at each level, by using the  
relationship beta = VAR(X)^{-1}COV(X,Y). For example, the posterior  
distribution of the regression coefficients at the phylogenetic level  
would be:

reg.coef<-function(x, X=1:3, Y=4){
V<-matrix(x,c(X,Y),c(X,Y))
solve(V[X,X], V[X,Y])
}

apply(m1$VCV[,1:16], 1, reg.coef)

The model doesn't deal with measurement error on the individual  
measurements, but if you had repeat measurements per individual you  
could also fit these (as a diagonal matrix, rather than unstructured).

After taking into account measurement error, some people suggest that  
species.ide should be dropped from the model. I am not completely  
convinced by this argument.

Priors are going to be a pain in this model.

You could replace the us structures by ante3 structures. The model is  
then fitted directly in terms of the regression coefficients.  
Antedependence regression coefficients 3,5,6 are the regressions of  
X3, X2 and X1 on Y. If you are interested in this we have a  
mini-tutorial associated with a recently submitted paper I can send you.

Cheers,

Jarrod

Quoting Alberto Gallano <alberto.gc8 at gmail.com> on Sun, 3 Jan 2016  
15:45:26 -0500:

MCMCglmm error-in-variables (total least squares) model?

Thread (8 messages)