I posted a -ml- program that does a multinomial logit on statalist some
time ago:
http://www.stata.com/statalist/archive/2007-05/msg00449.html
Hope this helps,
Maarten
--- Bob Hammond <[email protected]> wrote:
> 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/
> *
> * For searches and help try:
> * http://www.stata.com/support/faqs/res/findit.html
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>
-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands
visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434
+31 20 5986715
http://home.fsw.vu.nl/m.buis/
-----------------------------------------
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*
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