Hi,
I wrote a program that successfuly computes the maximum likelihood
estimates of the coefficients of a logisitc regression for binary response.
I verified the results using Minitab and SPSS. When I tried to implement the
algorithm for the Multinomial case, it didnt seem to be working properly.
The formula that updates the coefficients is the following:
Beta(t+1)=B(t)+{X' Diag[Pi(i)*(1-Pi(i))] X}^-1 X' (y-Pi(i))
where Beta(t) is the coefficients at iteration t,
pi(i) =exp(Sum {Beta(j)*Xij}/(1+exp(Sum {Beta(j)*Xij})
The question is how to compute the maximum likelihood coefficients for the
multinomial case?, assume I have 5 categories in the response and 1
independent (with 250 samples with 50 for each category). Lets say I pick
category 5 as the reference category and I want to estimate the logit
coefficients for category 1. Do I exclude all the records belonging to other
categories (i.e. 2,3,4) and compute the maximum likelihood coefficients for
1 and 5 only.... the problem when I tried that I got estimates different
from the ones that SPSS and Minitab got. Can someone shed some light on
this matter? Thanks.
Sincerely,
falbinali
.
.
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