On 16-Jan-03 Ted Harding wrote: > Hence the multivariate regression model for the data could be > written in matrix form as > > Y = X*B + w1*W1 + w2*W2 + w3*W3 + e > [ Y Nxp ; X Nxk ; W1 W2 W3 Nxp matices of factor level indicators; B kxp ; w1, w2, w3 scalars ]
> where e is 3-dim N(0,S), and B, w1, w2, w3 and S are to be estimated. > > What, in R, I can't make out how to do is to give some function > (which function?) a model specification of the form > > Y ~ X + W1 + W2 + W3 > > but in such a way that it will fit a 2x3 matrix B of coefficients for > X, but scalar coefficients w1, w2, w3 for W1, W2, W3 I think the thought underlying my query was that, if R would accept designating a _matrix_ of factor levels as a factor while preserving its matrix structure, then the above could fit into the model specification scheme. However, factor(W1), for instance, returns a linear structure. Apologies for the typo originally in the formula below (now corrected): > Analytically, the log-likelihood can be written (summing over r) > > (-N/2)*log(det(S)) - 0.5*SUM[ e_r * S^(-1) * e_r' ] (e_r = rth row) > > where e = Y - B*X - w1*W1 - w2*W2 - w3*W3. After differentiation and > algebra, one could implement the resulting matrix equations in octave > (or matlab) and proceed to a solution. One could even do this, as a > numerical procedure, in R -- but I'd rather not! Indeed, R's richness > in model-fitting resources tempts one to think that this problem may > be solvable using these -- it's just that I can't seem to put my hand > on what's needed. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 167 1972 Date: 17-Jan-03 Time: 09:09:46 ------------------------------ XFMail ------------------------------ ______________________________________________ [EMAIL PROTECTED] mailing list http://www.stat.math.ethz.ch/mailman/listinfo/r-help