I would like to specify a multivariate model with `lme`

with a random effect for group which is independent across variables. I found this post,

which explains that the model specified as:

`fit.multilevel <- lme( y ~ var -1, dd, random = ~ var -1| school, correlation = corSymm( form = ~ v |school/id), weights = varIdent(form = ~ 1 | v)) `

is equivalent to (using `MCMCglmm`

):

`fit.w.null <- MCMCglmm( cbind(mathach, ses) ~ trait -1 , random = ~us(trait):school, rcov = ~us(trait):units, data = hs, family = c("gaussian","gaussian")) `

However the model I would really like has independent random effects for school across the variables:

`fit.w.null <- MCMCglmm( cbind(mathach, ses) ~ trait -1 , random = ~idh(trait):school, rcov = ~us(trait):units, data = hs, family = c("gaussian","gaussian")) `

(the random effect is specified with `idh()`

). I cannot find a way to specify this in `lme`

.

Here is some code to generate example data and run the analysis:

`gr=rep(c("A","B","C"),each=100) grp.mean=rep(rnorm(3,5,1),each=100) var1=rnorm(300,rep(rnorm(3,5,1),each=100),1) var2=0.8*var1+3*rnorm(300,rep(rnorm(3,5,1),each=100),2) dat.mcmc=data.frame(var1=var1,var2=var2,group=gr) dat.lme=data.frame(y=c(var1,var2),var=rep(c("1","2"),each=length(gr)), group=rep(gr,2),id=rep(1:length(gr),2)) dat.lme$v=as.integer(dat.lme$var) `

Currently this is the best I can do:

`fit.multilevel <- lme( y ~ var -1, dat.lme, random = ~ var -1| group, correlation = corSymm( form = ~ v |group/id), weights = varIdent(form = ~ 1 | v)) `

This is (I believe) equivalent to:

`fit.w.null <- MCMCglmm( cbind(var1, var2) ~ trait -1 , random = ~us(trait):group, rcov = ~us(trait):units, data = dat.mcmc, family = c("gaussian","gaussian")) `

However, I would like an `lme`

command equivalent to:

`fit.w.null <- MCMCglmm( cbind(var1, var2) ~ trait -1 , random = ~idh(trait):group, rcov = ~us(trait):units, data = hs, family = c("gaussian","gaussian")) `

Any help you can give me will be much appreciated.

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