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Beyond the fact that the the two methods have different assumptions :

  • Logistic on the residuals extrem value distribution & utility theory.
  • QDA on the predictors multivariate gaussian distribution with specific covariance matrix for each classe.

Which determines how we estimate the coefficients :

  • In logistic regression by maximum Likelihood methods.

  • In QDA by Bayes discriminant classifier technique.

But it end up that they have a quite similar discriminant function when it is stated quadratic and interraction relations between predictors (let's say for all predictors).

for instance it is obvious when we take a comparison of the Log(P(Y= k|X)/P(Y= l|X) of both Logistic regression and QDA.

As mentionned in the title are they similare in this special case ? Or there is other subtil details which I have ommited/misleading ?

If they are similar (analytically) what about their prediction performance ?

  • In my intuition is that logistic outperform QDA when the normal distribution hypothesis does not hold, because of the estimation coefficient relies on the maximum likelihood (less restricted than assert multivariate normal distribution of predictors), I wonder if I got it ?
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