On 21-Aug-09 18:12:45, megh wrote: > > "Y" is 2 dimensional vector, X1 and X2 are 2x2 matrices.
Sorry -- I mis-read your code! I will think about your problem. Apologies. Ted. > 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-tp25083103p250 > 84866.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. -------------------------------------------------------------------- E-Mail: (Ted Harding) <ted.hard...@manchester.ac.uk> Fax-to-email: +44 (0)870 094 0861 Date: 21-Aug-09 Time: 18:59:54 ------------------------------ 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.