A new feature in MCMCglmm version 2.18 is block diagonal residual structures.

Jarrod Hadfield:

Block Diagonal R-structures are now allowed. For example imagine a bivariate model where pairs of observations are made on individuals of different sex. There may be a need to fit different 2x2 residual covariance matrices for the two sexes.

`rcov=~us(trait:sex):units`

would fit a 4x4 covariance matrix, but the between-sex residual covariances would be estimated despite not being identifiable (no individual can be both sexes). Now, models of the form`rcov=~us(trait:at(sex, "M")):units+us(trait:at(sex, "F")):units`

can be fitted that allow the non-identified covariances to be effectively set to zero.

In other words, previously if you had 2 traits measured for females and males and you wanted to fit a sex specific residual with `rcov=~us(trait:sex):units`

you would end up with a residual matrix like

for the variances (V) and covariances (cov) of females traits f_{1} and f_{2} and male traits m_{1} and m_{2}. The bold components are estimable from the data while the red ones are not. However, because of the way the residual is set up MCMCglmm will try to estimate the red parameters as well.

With block diagonals, you are specifying a matrix like

where the gray cells are now ignored. This is accomplished by fitting two 2 × 2 matrices for the R structure then having separate terms in the `rcov`

formula