(Since there were some small errors in the previous text
I just send a complete correction. Pls excuse for inconvenience)
"Arthur J. Kendall" schrieb:
>
> It is unusual.
> SPSS has had PCA under FACTOR since at least 1972.
> include the specification
> /extraction = PC
> or equivalently
> /extraction = PA1
> on the FACTOR procedure.
>
> I don't know if it can handle 11,000 variables.
>
It would need a *lot* of time and memory (at least ~121*16 MB, only for the
correlation matrix.
I remember to have read articles about "large matrices" or "large spare matrices"
some years ago... Search via google, also in sci.stat.consult. They talked about
these matrix-dimensions.
Concerning 150 cases with 11000 variables : you just get at most 150 factors, and
have linear dependencies after that.
If nothing helps, you could do a PCA on the first 150 variables and save the
scores.
Then you can correlate all variables with the factor scores and put the
correlations together to form a proper factor-loadingsmatrix. This way you can use
as much variables as your program can handle per run. Putting them all together this
gives you a factor-loadings-matrix of 11000*150 (~26 MB per matrix), which might be
*a little* better to handle than 11000*11000. With SPSS you can read a ready factor-
loadingmatrix directly into the procedure
Only you don't get factor scores then. If you need them, you can use the matrix-
language facility to build the pseudoinverse of your final factor-loadings matrix,
(this has one dimension of only 150) and matrix-multiply this with your raw-data.
Say
V - Array of all 11000 Variables,variables verical, cases horizontal
--------------------
V1 - Array of first 150 variables
V2 - Array of next 150 variables
...
then
R = corr(V1,V1')
L0 = cholesky(R) // compute loadingsmatrix, for instance with chlesky method
I0 = inv(L0) // inverse of loadingsmatrix for scores-calculation
Fsc1 = I0*V1 // compute raw scores for your 150 factors
now compute loadings for all variables. Their loadings are the
correlations between factors and variables:
Lad1 = corr(Fsc0,V1) // loadings for the first 150 variables
Lad2 = corr(Fsc0,V2) // loadings for the next 150 variables
...
Ladx = corr(fsc0,Vx) // loadings for the last 150 variables
put them all together to have a combined loadingsmatrix for rotations
Lad = {L1,L2,L3...}
After that you can perform the rotations.
-----------
To get scores, you use matrix-algebra:
Since
[1] Lad * Fsc = V
[2] Lad'*Lad * Fsc = Lad' * V // here Lad'*Lad is of 150*150
[3] ILad = inv(Lad'*Lad)
[4] ILT = ILad*Lad'
[5] Fsc = ILT * V
you can get factor-scores just by multiplying your variable-values
by the matrix ILT, which has one dimension of only 150 at most.
HTH
Gottfried Helms
.
.
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