>From the equation you write, I don't see why "lsfit" wouldn't work. To estimate the covariance matrix of e you could use the sample covariance matrix of the residuals. If desired, use its cholesky decomposition to transform to make the error approximately uncorrelated, then refit (and back-transform the coefficient matrix).
Stacking the columns of Y and replicating X won't do what you write; it forces each univariate regression to have the same coefficients. To get what you wrote you would replicate X in blocks of a block-diagonal matrix. I'm not sure I understand the role of W. If what you want is to fit equations like y(i) = a(w(i)) + xB(i) + e(i) for each observation and each response y(1),...,y(p), then I guess you could just fit each response separately, treating W as a factor. Then estimate the covariance matrix of e via the residuals as before, etc. Reid Huntsinger -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]] Sent: Thursday, January 16, 2003 10:16 AM To: [EMAIL PROTECTED] Subject: [R] Multivariate regression in R Hi Folks, I want to do multivariate regression in R, i.e. basically (but with a complication -- see below): given an Nxp matrix Y of p-variate responses, and an Nxk matrix X of covariates, to fit the model Y = X*B + e with estimation of the kxp matrix of coefficients B and estimation of the pxp matrix of covariances between the p variates in Y. I haven't managed to find a function/package in R which seems to address this problem directly (maybe I'm overlooking a way of using a standard one). One way, of course, could be to stack the columns of Y on top of each other, replicate X vertically accordingly, and try to introduce a suitably structured covariance matrix; but I would like to think that there's an easier way ... ! The complication: for each row of Y, each of the p variates is associated with one level of a p-level factor W (on a permuted basis, so that y1,...,yp are associated with levels i1,...,ip of W where (i1,...,ip) is a permutation of levels (1,...,p) of W). I'm wondering, too, how to represent this in R. In the univariate case, for instance, the matrix representation for a factor when regressing y on r levels of a factor F represents the factor as an Nxr matrix with zeros except for 1s in col j for rows where y has the level j of F. In the multivariate case, each row of Y would by analogy be associated with a matrix of factor levels, one row for each variate in Y, so as to pick out the factor levels by columns as in the univariate case for that variate. Any help/advice would be much appreciated! With thanks, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 167 1972 Date: 16-Jan-03 Time: 15:16:12 ------------------------------ XFMail ------------------------------ ______________________________________________ [EMAIL PROTECTED] mailing list http://www.stat.math.ethz.ch/mailman/listinfo/r-help ------------------------------------------------------------------------------ ______________________________________________ [EMAIL PROTECTED] mailing list http://www.stat.math.ethz.ch/mailman/listinfo/r-help
