Talk:Multinomial logit

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This page appears to fail to recognize the existance of ordered multinomial responses, no? Pdbailey 02:15, 12 June 2007 (UTC)

[edit] I corrected a mistake in the denominator

In the Model, we better have the probabilities adding to 1:

\sum_{j=0}^{J} Pr(y_i=j) = 1

That means the denominator needs to be:

1+\sum_{j}^{J}\exp(X_{i}\beta_{j})

and not just

\sum_{j}^{J}\exp(X_{i}\beta_{j})

The 1 here is the contribution from Pr(yi = 0).

By the way, I'm used to thinking of Xi as a vector, in which case X is a matrix, βj is a vector, and Xiβj is a dot-product. The way these equations are written imply that Xi and βj are scalars, which is okay if you are predicting y from a single scalar X. I found that a bit confusing and had to stare at it a bit longer than usual to parse it. Some clarification about this might be helpful in the article.