Dear all,

Is it possible to extract the residual variance not explained by two
discriminant axes?

Here is my setup:
1. I constructed a linear discriminant space based on 16 continuous traits
measured for 3 species using the lda function from the MASS package (3
species ~ 16 traits). 3 categories = 2 discriminant axes.

2. I measured the same traits for hybrids and plotted them on these two
axes using the predict function on the lda object.

3. I want to extract residuals for these hybrids not explained by the two
lda axes.

Is this possible? The overall goal is to run additional analyses on the
residual variation in the 16-trait dataset not explained by the 2
discriminant axes.

The two discriminant axes are not orthogonal, so I cannot perform two
linear regressions and extract residuals. I tried performing manova on the
16 traits measured on the hybrids with the 2 discriminant axes as
independent variables, but I get the error "residuals have rank 14 < 16".

Any pointers or suggestions would be greatly appreciated! Please let me
know if clarification is needed.

thanks!
Chris

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