Multivariate Weighted Linear Regression Very simple.  I am looking for a package that does Multivariate Linear Regression with weights on the observations.  Does anyone know of a package that does this?  I am shocked that I have not been able to find any.
NOTE:  R does NOT do multivariate regression.  The lm() help page specifically states:  "If response is a matrix a linear model is fitted separately by least-squares to each column of the matrix. "  This means independent regression models for each response variable.  Thus lm()  does NOT do multivariate linear regression.  It merely does several univariate linear regressions for convenience.
 A: Try package MRCE in R. This is for "Multivariate regression with covariance estimation".
A: Case weights in a multivariate (multiple-outcome) regression don't have the straightforward meaning that they have in weighted least squares with a single outcome variable. Then each weight ideally represents the inverse of the variance of the corresponding outcome value, with error variances independent among cases. In a multivariate regression such an interpretation of a case weight would implicitly assume that all outcomes had the same relative variances from case to case. Also, a major reason for multivariate regression is to estimate the covariances among outcome values.
A work-around would be to take advantage of how, with a single outcome, a data transformation followed by OLS provides the same regression coefficients as weighted least squares. If you pre-multiply each of the design matrix and the outcome vector by the diagonal matrix of the square roots of the case weights, then OLS gives the same result as weighted least squares. As the regression coefficients returned by multivariate regressions are the same as those produced by regressions with each of the outcome variables individually, just extend that to pre-multiplying the outcome matrix--if you are willing to accept the consequences of any inapplicability of case weights to a multivariate regression. Transform the data first, then do the mulitivariate regression.
Despite the fear raised by the OP, lm() handles unweighted multivariate regressions quite well. It produces "mlm" objects that contain all the information needed for standard multivariate inference. See Fox and Weisberg. The R stats package simply (and I expect for reasons noted above) refuses to process a weighted multivariate regression beyond the estimation of the coefficients.
A: This is an old post, but the OP is factually wrong in claiming R doesn't do multi-variate regression.
The documentation states "If response is a matrix a linear model is fitted separately by least-squares to each column of the matrix."  The key thing here is RESPONSE is a matrix.  That is the Y is a matrix, then  R fits ncol(Y) separate models to the same X: Y(i) ~ X.
