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# Re: st: (non-Stata) mixture of probits

 From [email protected] To [email protected] Subject Re: st: (non-Stata) mixture of probits Date Wed, 29 Dec 2004 15:32:13 -0600

```"Mixture of Normals Probit Models" John Geweke and Michael Keane

ABSTRACT
This paper generalizes the normal probit model of dichotomous choice by introducing mixtures of normals distributions for the disturbance term. By mixing on both the mean and variance parameters and by increasing the number of distributions in the mixture these models effectively remove the normality assumption and are much closer to semiparametric models. When a Bayesian approach is taken, there is an exact finite-sample distribution theory for the choice probability conditional on the covariates. The paper uses artificial data to show how posterior odds ratios can discriminate between normal and nonnormal distributions in probit models. The method is also applied to female labor force participation decisions in a sample with 1,555 observations from the PSID. In this application, Bayes factors strongly
favor mixture of normals probit models over the conventional probit model, and the most favored models have mixtures of four normal distributions for the disturbance term.

Hope this helps,
Scott

----- Original Message -----
From: "FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" <[email protected]>
Date: Wednesday, December 29, 2004 11:57 am
Subject: st: (non-Stata) mixture of probits

> Hello - Does anyone know of work on a probit-like model that uses
> a mixture
> of two normals, rather than one normal distribution as the latent
> variabledistribution? If so, is there an extension to random effects?
>
> P(Y = 1 |X) = norm(Xbe + e) where e ~ mixture of two normals
>
>
>
> This would arise if e comes from one of two populations depending
> on another
> unobservable dichotomous RV.
>
> Al Feiveson

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