CANCORR (Canonical Correlations)

[TomDoan]

The following is a procedure for doing general canonical correlation analysis.

Code: Select all

*
* @CANCORR( options ) start  end
* # list of "Y" variables (regression format)
* # list of "X" variables (regression format)
* # list of conditioning variables (regression format, if CONDITION option)
*
* Computes the canonical correlations and related statistics for two sets of
* series, possibly conditioning on the third set.
*
* Parameters:
*
*  start end      range to use. By default, the maximum range allowed by the
*                 variables involved.
*
* Options:
*  CENTER/NOCENTER  If CENTER, the means are subtracted from the variables before
*      computing the covariance matrix. The default is CENTER unless you use the
*      CONDITION option.
*  CONDITION/[NOCONDITION] If CONDITION, the covariance matrix analyzed is that of
*      the residuals from a regression on the conditioning set of variables. This
*      will generally include the CONSTANT (so residuals will be mean zero) in
*      addition to the other variables.
*  EIGENVALUES=(output) VECTOR of eigenvalues, ordered from high to low. These will
*      all be >=0 and <=1.
*  VECTORS=(output) RECTANGULAR of eigenvectors for the X variables. Column <<i>> has
*      the weights for canonical component <<i>> of the X's.
*  DUALVECTORS=(output) RECTANGULAR of eigenvectors for the Y variables. Column <<i>>
*      has the weights for canonical component <<i>> of the Y's.
*  LOADINGS=(output) RECTANGULAR of coefficients on a multivariate regression of the
*      Y's on the canonical components of the X's. Element (i,j) has the coefficient
*      for component j of the X's in the regression for Y.
*
*  Revision Schedule:
*   03/2008 Written by Tom Doan, Estima.
*
procedure cancorr start end
type integer start end
*
option switch center    1
option switch condition 0
*
option rect   *vectors
option rect   *dualvectors
option vect   *eigenvalues
option rect   *loadings
*
local equation xtemp
local equation ytemp
local equation ztemp
local equation combined
local rect     eigvec dualvec
local vect     eigval
*
local rect s s01
local symm s00 s11
local symm s10_00_01 s01_11_10
*
local int  nx ny nz
*
* Get the two main sets of variables
*
equation ytemp *
equation xtemp *
compute ny=%eqnsize(ytemp)
compute nx=%eqnsize(xtemp)
*
* Combine them into a single list for computing the cross product matrix.
*
compute combined=ytemp+xtemp
*
* If <<condition>>, get the third set of variables, and append it to the combined
* list.
*
if condition {
  equation ztemp *
  compute combined=combined+ztemp
  compute nz=%eqnsize(ztemp)
}
*
* Compute the grand crossproduct matrix and divide through by the number of
* observations to get the raw covariance matrix.
*
cmom(center=center.and..not.condition,equation=combined) start end
compute s=%cmom*(1.0/%nobs)
*
* If <<condition>>, sweep out the conditioning set of variables
*
if condition
   compute s=%sweeplist(s,%seq(nx+ny+1,%ncmom))
*
* Pull out the required submatrices from the block of the y and x variables.
*
compute s00=%xsubmat(s,   1,ny   ,   1,ny)
compute s11=%xsubmat(s,ny+1,ny+nx,ny+1,ny+nx)
compute s01=%xsubmat(s,   1,ny   ,ny+1,ny+nx)
*
* Compute the generalized eigenvalues and vectors. The first calculation gets the
* canonical components for the "X" variables.
*
compute s10_00_01=tr(s01)*inv(s00)*s01
eigen(general=s11) s10_00_01 eigval eigvec
*
* Save the parts that the user wants
*
if %defined(eigenvalues)
   compute eigenvalues=eigval
if %defined(vectors)
   compute vectors=eigvec
if %defined(loadings)
   compute loadings=s01*eigvec
*
* If we want the dual vectors as well, compute the reverse problem and save the
* eigenvectors.
*
if %defined(dualvectors) {
   compute s01_11_10=s01*inv(s11)*tr(s01)
   eigen(general=s00) s01_11_10 eigval dualvec
   compute dualvectors=dualvec
}
end