R help - Jul 2016 - Including correlation between weights in multivariate regression

Dear Rusers,

We want to fit a multivariable normal distribution to multiple observation
variables, where these are observed with uncertainty represented by a covariance
matrix which is different for each individual.

An example dataset (simplified) might look like this:
set.seed(101010)
nobs=20
test.data <- data.frame(ID=1:nobs,
                        y1=rnorm(n=nobs, mean=0, sd=0.15),
                        y2=rnorm(n=nobs, mean=0.15, sd=0.20),
                        var11=abs(rnorm(n=nobs, mean=0.1, sd=0.0011)),
                        cov12=rnorm(n=nobs, mean=0.001, sd=0.0001),
                        var22=abs(rnorm(n=nobs, mean=0.1, sd=0.0012)))

Where varX are the uncertainties of the observations (in variance units), and
cov is covariance between the variance for the first and the second column (i.e.
dependent variable).

One can do something like this, using lm, if we include only a single weight:
lm(cbind(y1, y2) ~ 1, data = test.data, weights = 1/test.data$var11)

But we would like to include different weights for each of the dependent
variables, and also correlation between the weights.  Additionally, we may have
up to ~30 observation variables (y1 through y30). Does anyone have any
experience with this, or know a package that can do that?

Many thanks.

Best wishes,

Eva




Eva Germovsek, PhD
Pharmacometrics Research Group
Department of Pharmaceutical Biosciences
Uppsala University
P.O. Box 591
751 24 Uppsala
Sweden

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