"Y" is 2 dimensional vector, X1 and X2 are 2x2 matrices.
Ted.Harding-2 wrote: > > On 21-Aug-09 16:28:26, megh wrote: >> Hi, I have following kind of model : Y = X1 * a1 + X2 * a2 + error >> >> Here sampled data for Y, X1, X2 are like that : >> >> Y <- replicate(10, matrix(rnorm(2),2), simplify = F) >> X1 <- replicate(10, matrix(rnorm(4),2), simplify = F) >> X2 <- replicate(10, matrix(rnorm(4),2), simplify = F) >> >> My goal is to calculate LS estimates of vectors "a1" and "a2". >> Can anyone please guide me how to do that in R? Is there any >> special function to handle this kind of problem? >> >> Thanks > > In your example, a1 and a2 cannot be vectors, since Y, X1 and X2 > are all 2x2 matrices. On the other hand, either or both of a1, a2 > could be either a scalar or a 2x2 matrix, any of which would make > X1*a1 + X2*a2 (provided you interpret "*" as "%*%" in R) into a > 2x2 matrix. But if (say) a1 is a vector it can only be a 2x1 > vector (for multiplication conformity), and then X1*a1 (or X1%*%a1 > in R) would be a 2x1 vector (in the linear algebra sense, i.e. > a 2x1 matrix in the R sense). > > So what is it that you want in the model? > > Next, if in fact a1 and a2 are scalars, then in effect you are > looking at > > Y1[1,1] = a1*X1[1,1] + a2*X2[1,1] + error[1,1] > Y1[1,2] = a1*X1[1,2] + a2*X2[1,2] + error[1,2] > Y1[2,1] = a1*X1[2,1] + a2*X2[2,1] + error[2,1] > Y1[2,2] = a1*X1[2,2] + a2*X2[2,2] + error[2,2] > > 10 times over. The relevant question here is: Are you wanting > to include possible covariance between the 4 elements of 'error'? > > One possibility in this case is to treat this as a multilevel > or longitudinal model, with 4 observations "per subject", and > correlated error within-subject. > > But you really need to spell out more detail of the kind of > model you are seeking to fit. What you described is not enough! > > Ted. > > -------------------------------------------------------------------- > E-Mail: (Ted Harding) <ted.hard...@manchester.ac.uk> > Fax-to-email: +44 (0)870 094 0861 > Date: 21-Aug-09 Time: 18:48:31 > ------------------------------ XFMail ------------------------------ > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > -- View this message in context: http://www.nabble.com/%22Special%22-LS-estimation-problem-tp25083103p25084866.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
