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# Re: st: RE: RE: Discrete choice in MATA

 From Matthew Baker To statalist@hsphsun2.harvard.edu Subject Re: st: RE: RE: Discrete choice in MATA Date Tue, 25 Jun 2013 09:46:22 -0400

```Henk-Wim --

I'm not sure if someone else took a crack at this, but I think that
the following might help a little. First, I might make two suggestions
that I have found useful in these cases. First, I would work with data
in the wide form, not the long form, as you have it. You can convert
it using reshape, or some of the functions that come with the
"case2alt" package by Scott Long and Jeremy Freese. (net search
case2alt). I just use reshape in the little example below.

Second, I might suggest working with moptimize instead of optimize, as
this eases transferring data from stata to mata, and having to parse
all of the parameters in beta yourself. Here's a little example of a
multinomial logit model. I "difference" the independent variable and
normalize the utility from the first option to zero:

/* Begin example */

clear all
webuse choice

/* reshape data */
bysort id: gen t=_n
reshape wide car size choice dealer, i(id) j(t)

/* differences */
gen dealer2m1=dealer2-dealer1
gen dealer3m1=dealer3-dealer1

mata
void logistic(M, b, fv)
{
real scalar i
real matrix y1, y2, y3, xb2, xb3
y1=moptimize_util_depvar(M,1)
y2=moptimize_util_depvar(M,2)
y3=moptimize_util_depvar(M,3)
xb2=moptimize_util_xb(M,b,1)
xb3=moptimize_util_xb(M,b,2)
num=rowsum(y1:+y2:*exp(xb2):+y3:*exp(xb3))
den=rowsum(1:+exp(xb2):+exp(xb3))
fv=ln(num:/den)
}

M=moptimize_init()
moptimize_init_evaluator(M,&logistic())
moptimize_init_evaluatortype(M,"lf")
moptimize_init_depvar(M,1,"choice1")
moptimize_init_depvar(M,2,"choice2")
moptimize_init_depvar(M,3,"choice3")
moptimize_init_eq_indepvars(M,1,"dealer2m1")
moptimize_init_eq_indepvars(M,2,"dealer3m1")
moptimize(M)
moptimize_result_display(M)
end

/* End example */

Hope that helps!

Matt

On Fri, Jun 21, 2013 at 6:53 AM, Henk-Wim de Boer <H.W.de.Boer@cpb.nl> wrote:
> Hi Tim,
>
> The reason for this is that I am using simulated maximum likelihood, where I use 10 draws from the wage distribution. In addition, I extended our basic labour supply model with 4 additional alternatives for childcare.
> I end up with 24 alternatives for singles and 144 alternatives for couples. I estimate the model, using a large rich dataset, with a lot of alternatives and parameters. Consequently, the estimation for couples takes approximately 4 days. In the future, I want to increase the number of draws from the wage distribution as well and therefore I want to speed up the estimation.
>
> I tried so by deriving the first and second order derivatives analytically (ml model d1 and d2) but this did not work for multiple draws from the wage distribution. The model only converges if I allow for 1 draw and not for multiple draws. It seems that rounding errors prevent the model from converging (the first derivative is close to 0 and remains close to 0). Now I want to program it in Mata.
>
> Henk-Wim
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Timothy Mak
> Sent: 21 June 2013 04:12
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: Discrete choice in MATA
>
> Hi,
>
> Discrete choice models are well-covered by Stata commands such as -clogit- and -asclogit-.
> http://www.ats.ucla.edu/stat/stata/seminars/stata10/choice_models.htm
>
> Why do you want to implement them yourself?
>
> Tim
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Henk-Wim de Boer
> Sent: 20 June 2013 22:37
> To: 'statalist@hsphsun2.harvard.edu'
> Subject: st: Discrete choice in MATA
>
> 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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> ================================================================================
> Dit bericht kan informatie bevatten die niet voor u is bestemd. Indien u niet
> de geadresseerde bent of dit bericht abusievelijk aan u is toegezonden, wordt
> u verzocht dat aan de afzender te melden en het bericht te verwijderen.
> De Staat aanvaardt geen aansprakelijkheid voor schade, van welke aard ook, die
> verband houdt met risico's verbonden aan het elektronisch verzenden van
> berichten.
>
> This message may contain information that is not intended for you. If you are
> not the addressee or if this message was sent to you by mistake, you are
> requested to inform the sender and delete the message. The State accepts no
> liability for damage of any kind resulting from the risks inherent in the
> electronic transmission of messages.
> ================================================================================
>
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--
Dr. Matthew J. Baker
Department of Economics
Hunter College and the Graduate Center, CUNY

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```