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# st: Discrete choice in MATA

 From Henk-Wim de Boer <[email protected]> To "'[email protected]'" <[email protected]> Subject st: Discrete choice in MATA Date Thu, 20 Jun 2013 16:36:42 +0200

```Hello,

I am relatively new at MATA and I am trying to program maximum likelihood estimation for my discrete choice model.
The labour supply model allows for 6 labour supply alternatives at the individual level and an example is included below for an individual:

Id            h         y_1            l
1            0            2           80
1             8            4           72
1             16           6           64
1             24           8           56
1             32          10           48
1             40          12           40

The model can be estimated by maximum likelihood, where the log likelihood is as follows: ln(L) = ln{ exp(xb)/sum(exp(xb)) } over all individuals.
This works well in STATA by using ml model but I now want to program it in MATA. The difficulty here is constructing the denominator, i.e  the summation of exp(xb) over all alternatives.

My code is as follows:

mata

st_view(X=0,.,("lny_1", "lnl"))
st_view(y=0,.,("choice"))

void logistic(todo, p, y, X, lf, g, H)
{
b = p[1, (1::cols(X))]'    /* Transpose such that b is a column vector*/

denom = colsum(exp(X*b)) /*HERE I NEED TO SUM OVER THE ALTERNATIVES PER INDIVIDUAL , WHICH DOES NOT WORK FOR ME*/

lf = y' * ln(exp(X*b)/denom)

}

S = optimize_init()
optimize_init_evaluator(S, &logistic())
optimize_init_params(S, (0, 0))     /* One extra element. Starting values are (0, 0)*/
optimize_init_argument(S, 1, y)
optimize_init_argument(S, 2, X)
p = optimize(S)

p

end

Henk-Wim de Boer

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