[R] Penalized Canonical Variates

[Frank E Harrell Jr]

In the excellent paper by Hastie, Buja, and Tibshirani "Penalized 
Discriminant Analysis" the authors developed penalized discriminant 
functions that incorporated shrinkage on the predictor parameters.  This 
is a shrunken version of a canonical correlation analysis in which dummy 
variables appear on the left hand side.  Canonical variates are 
frequently overfitted and in some cases shrinkage is needed 
simultaneously on the left and right hand sides.  For example, one may 
have a multi-group discrimination problem where some of the groups have 
low frequencies and need to borrow information from the other groups. 
As another example, if one generated data from the linear model Y = X + 
residual and found optimum transformations of X and Y that maximized R^2 
  using canonical variates allowing for quadratic transformations, a b c 
d are solved for in the multivariate regression aY^2 + bY = cX^2 + dX. 
  Without penalization, the fitted model will be too nonlinear for small 
sample sizes.  Penalizing nonlinear terms would help.  Does anyone know 
of a method or code that does both-sides penalization for canonical 
variates (multivariate least-squares regression)?

Thanks
Frank
-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University