st: question on MLE d0 method for multilogit model with invariant regressors

[Hey Sky <heyskywalker@yahoo.com>]

Hey, All


I try to do a mle d0 estimation for multilogit model with invariant regressors and have searched internet but no luck. I wish I can get some help here. any suggestion is appreciated. 

here is the question:

given a period, the probability of a person choose choice k is:

pr(choice=k)=exp(x*beta_k)/(exp(x*beta_1) + exp(x*beta_2)+...)

that is, the regresors are invariant, x, but the parameters are variant when choose diffecrent choice, beta_1, beta_2, etc.  

a little complicated case is when making the regressors and parameters both changes along with choices, i.e.

pr(choice=k)=exp(x_k*beta_k)/(exp(x_1*beta_1) + exp(x_2*beta_2)+...)

how to do it with the Stata MLE method? thanks for any clue you provide. 

Nan
from Montreal


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