[R] logistic discrimination: which chance performance??

[Bruno L. Giordano]

Hello,
I am using logistic discriminant analysis to check whether a known 
classification Yobs can be predicted by few continuous variables X.

What I do is to predict class probabilities with multinom() in nnet(), 
obtaining a predicted classification Ypred and then compute the percentage 
P(obs) of objects classified the same in Yobs and Ypred.

My problem now is to figure out whether P(obs) is significantly higher than 
chance.

I opted for a crude permutation approach: compute P(perm) over 10000 random 
permutations of Yobs (i.e., refit the multinom() model 10000 times randomly 
permuting Yobs) and consider P(obs) as significantly higher than chance if 
higher than the 95th percentile of the P(perm) distribution.

Now, the problem is that the mode of P(perm) is always really close to 
P(obs), e.g., if P(obs)=1 (perfect discrimination) also the most likely 
P(perm) value is 1!!!

I figured out that this is due to the fact that, with my data, randomly 
permuted classifications are highly likely to strongly agree with the 
observed classification Yobs, but, probably since my machine learning 
background is almost 0, I am kind of lost about how to proceed at this 
point.

I would greatly appreciate a comment on this.

Thanks
    Bruno

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Bruno L. Giordano, Ph.D.
CIRMMT
Schulich School of Music, McGill University
555 Sherbrooke Street West
Montréal, QC H3A 1E3
Canada
http://www.music.mcgill.ca/~bruno/