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

Montr?al, QC H3A 1E3

Canada

http://www.music.mcgill.ca/~bruno/