[R] "Special" LS estimation problem
megh
megh700004 at yahoo.com
Fri Aug 21 20:12:45 CEST 2009
"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.Harding at manchester.ac.uk>
> Fax-to-email: +44 (0)870 094 0861
> Date: 21-Aug-09 Time: 18:48:31
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>
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