Chapter 9: Covariance Structures and Factor Analysis

FIMAG

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Computes the image transformation matrix.

Required Arguments

TNF by NF transformation matrix.   (Input)

TINF by NF image transformation matrix.   (Output)

Optional Arguments

NF — Number of factors.   (Input)
Default: NF = size (T,2).

LDT — Leading dimension of T exactly as specified in the dimension statement in the calling program.   (Input)
Default: LDT = size (T,1).

LDTI — Leading dimension of TI exactly as specified in the dimension statement in the calling program.   (Input)
Default: LDTI = size (TI,1).

FORTRAN 90 Interface

Generic:                              CALL FIMAG (T, TI [,…])

Specific:                             The specific interface names are S_FIMAG and D_FIMAG.

FORTRAN 77 Interface

Single:                                CALL FIMAG (NF, T, LDT, TI, LDTI)

Double:                              The double precision name is DFIMAG.

Description

Routine FIMAG computes the image transformation matrix TI from the factor rotation matrix (T). The image transformation matrix takes the unrotated factor loadings into the factor structure matrix when the unrotated loadings are computed from a correlation matrix. It is computed as the inverse of the transpose of the factor rotation matrix T. When orthogonal rotations are used,
(TT)1 = T so there is no reason to compute the image transformation matrix.

Comments

1.         Workspace may be explicitly provided, if desired, by use of F2MAG/DF2MAG. The reference is:

CALL F2MAG (NF, T, LDT, TI, LDTI, RWK, IWK)

The additional arguments are as follows:

RWK — Real work vector of length NF + NF(NF 1)/2.

IWK — Integer work vector of length NF.

2.         Informational Error

Type Code

3         1                  T is ill-conditioned. The solution may not be accurate.

Example

This example is a continuation of the example contained in the manual document for routine FROTA. The image transformation matrix is obtained from the orthogonal rotation matrix. Some small differences between the matrix TI when compared with the matrix T computed via routine FROTA can be seen. These differences are because of roundoff error since for orthogonal rotations, the image transformation matrix is the same as the rotation matrix.

 

      USE FIMAG_INT

      USE WRRRN_INT

 

      IMPLICIT   NONE

      INTEGER    LDT, LDTI, NF

      PARAMETER  (LDT=3, LDTI=3, NF=3)

!

      REAL       T(LDT,NF), TI(LDTI,NF)

!

      DATA T/.7307, .6816, -.0382, -.5939, .6623, .4569, .3367, -.3112, &
      .8887/

!

      CALL FIMAG (T, TI)

!

      CALL WRRRN ('TI', TI)

      END

Output

 

              TI
         1        2        3
1   0.7307  -0.5938   0.3367
2   0.6816   0.6622  -0.3112
3  -0.0382   0.4569   0.8887



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