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Re: st: Different likelihood estimates from -mixlpred- and own calculations using -mixlbeta-


From   Arne Risa Hole <arnehole@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Different likelihood estimates from -mixlpred- and own calculations using -mixlbeta-
Date   Wed, 12 Sep 2012 09:47:39 +0100

You are correct when you say that the"-mixlpred- likelihood is
averaged over simulated draws conditional on the coefficient
distribution estimates, rather than individual-specific coefficient
estimates" and this explains why the two approaches give different
results.

Yes, the approach you describe sounds reasonable if you want to
investigate how the probabilities change when the coefficient
estimates change.

Arne

On 7 September 2012 21:56, HSUEH-HSIANG 28Cher29 LI <hli37@wisc.edu> wrote:
> I’m having a problem with -mixlpred- in the -mixlogit- package. I obtained
> this user written program -mixlogit- by Arne Risa Hole with the updates from
> the SSC archive (I typed -ssc install mixlogit, replace- to get the
> updates). I am running the program on StataMP 12 for Windows.
>
> I run -mixlogit- on a panel data. After running -mixlogit-, I used the
> postestimation command -mixlpred- to get the likelihood of each option
> chosen by individuals in each period. In the meanwhile, I also obtained
> individual coefficient estimates using -mixlbeta-, and then calculate the
> likelihood using these inidvidual coefficients by individual and period:
> L_nit(beta_n)=exp(beta_n*X_nit)/[sum_{j=1,...J} exp(beta_n * X_njt)]
> (the equation is from Arne Risa Hole, 2007 "Fitting mixed logit models by
> using masimum simulated likelihood", The Stata Journal, 7, Number 3, pp.388)
>
> The predicted probabilities from -mixpred- and my own calculation using
> -mixlbeta- and the equation above are quite different. I am wondering how
> -mixpred- calculates the likelihood. It appears to me that this -mixlpred-
> likelihood is averaged over simulated draws conditional on the coefficient
> distribution estimates, rather than individual-specific coefficient
> estimates. Please correct me if I am wrong! Since I am interested in
> "simulating" how likelihood changes when coefficient estimates change, is it
> reasonable that I calculate the likelihood the way I mentioned above? Any
> suggestions and advice are welcomed!
>
> Sincerely,
> Cher
>

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