st: Multinomial logit-type probability in log likelihood for ML model

[Bob Hammond <robert.g.hammond@vanderbilt.edu>]

All,

I am having trouble coding an ML program for my log likelihood 
function.  I'll simplify several aspects of the log likelihood that seem 
unrelated to my question.  Define `lnf' for an individual observation as 
follows:

replace `lnf' = (Binomial(n,j,q) - Binomial(n,j+1,q)) * f(x)  if $ML_y1 == 1

In words, the probability that Y is 1 is the probability of observing 
exactly j successes out of n (where q is the probability of a success on 
an individual trial) times some function f(x).  The probability q takes 
a multinomial logit form:

q_i = exp(X_i * `theta') / (1 + sum(exp(X_h * `theta')))

where the sum goes from h=1, ..., J, so it sums the product of the 
covariate vector X times the parameter vector `theta' for all 
observations in the data set. 
It seems that I need some way to construct the summation in the 
denominator of q first, but my confusion is that this denominator 
contains the `theta' parameter vector.  Basically, for every observation 
in the data set, I need to construct a scalar that multiplies the 1 x k 
covariate vector X by the k x 1 parameter vector `theta' that needs to 
be estimated.  Then I need to sum these J scalars up (call this a, which 
is a function of `theta').  If I could do that, then, after constructing 
a, I would write:

replace `lnf' = (Binomial(n,j, exp(`theta') / (1 + a) - Binomial(n,j, 
exp(`theta') / (1 + a)) * f(x)
           if $ML_y1 == 1

I don't know how to construct "a" because it contains the parameter 
vector `theta'.  I've tried taking a look at the ado file for mlogit, 
but didn't find the answer.  Thanks in advance,

Bob
--
------------------------------------------------------------------------
Bob Hammond
Department of Economics
Vanderbilt University
http://people.vanderbilt.edu/~robert.g.hammond/
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