[R-sig-ME] bivariate response mixed model using lme4 and residual (co)variances

[Ben Bolker]

Ned Dochtermann <ned.dochtermann at ...> writes:

> 
> All,
> 
> I am attempting to "cheat" with lme4 to calculate the correlation between
> two traits--y & z--measured repeatedly (simulation data actually) for
> individuals by use of dummy variables. I can calculate the
> between-individual variances and covariances with the data structured as:
> 
> ind	y_rand		z_rand		yz
> A	1		0		-1.941248639
> A	1		0		0.747675528
> B	1		0		2.502358777
> B	1		0		2.752530485

  [snip]

> and then fitting the following model:
> 
> yz.mm<-lmer(yz~-1+y_rand+z_rand+(y_rand+z_rand-1|ind),data=ind.data)
> 
> This gives seemingly correct results (i.e. consistent with results from
> MCMCglmm and ASReml) for the between-individual estimates. The issue that
> I'm running into is that since I'm treating y and z as the same variable, I
> can't figure out how to get any sort of within-individual estimates beyond a
> single variance estimate. This makes sense given the way I've formulated the
> model. 
> 
> Is there any way to likewise cheat to get within-individual/group variance
> and covariance estimates with lme4? I can get what I need from MCMCglmm but,
> for computational reasons I'd prefer lme4. 
> 
> Thanks for any help,
> Ned
> 
> p.s. just realized that I can probably get what I want from lme...
> 

  Maybe displaying my ignorance, but is there a particular reason
to use dummy variables instead of a factor?  That is, if I start with

ind   y   z
A    1.2  2.4
A    1.3  2.1
B    2.1  3.2
B    2.3  4.6
...

and then use melt(data,id.var=1) from reshape I get data that look like

ind  variable value
A     y      1.2
A     z      2.4
A     y      1.3
A     z      2.1
....

and then 

lmer(value~variable-1+(variable-1|ind),data=ind.data) ?

it seems you could also add an "obs" variable to the original
data frame, use it as an id var as well, and be able to get a
correlation among observations taken at the same time within
the same individual ...