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From |
Maarten Buis <maartenlbuis@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: hetroscedasticity test after probit |

Date |
Thu, 5 Jul 2012 10:56:13 +0200 |

On Thu, Jul 5, 2012 at 10:32 AM, Yuval Arbel wrote: > Prakash, returning to your original question, I see no point at all to > check for hetroscedasticity after -probit- simply because this problem > is inherent in the family of models with binary dependent variables. > > Take, for example, the so called LPM (linear probability model), where > the dependent variable is derived from Binomial distribution (which > is by itself an approximation to the Normal distribution, from which > the probit model is derived). Every elementary Econometric textbook > (e.g. Jan Kmenta, Elements of Econometrics, 1997, pp. 548-549), will > show you a very simple proof revealing the fact that the LPM is > inherently heteroscdastic, where the variance of the random > disturbance term equals yhat(1-yhat) and yhat is the vector of > predicted values The problem is subtly but completely different with models like -probit- and -logit-. These models already use the variance function yhat(1-yhat), so there is no need to further adjust for that. However, heteroskedasticity is still a huge and unsolvable problem in these models. Think of it this way: your dependent variable is a probability. A probabiltiy embodies uncertainty, and that uncertainty comes from all variables we have not included in our model. In one sense this makes it very easy to deal with heteroskedasticity: We just define our dependent variable of interest to be the probability given the control variabels in our model. The results of your model give an accurate description of what you have found in your data. However, we often want to give parameters a counterfactual interpretation (e.g. "if the men suddenly became women, then the probabiltiy changes by x percentage points"). Such a counterfactual interpretation is only correct if we can assume that there is no heteroscedasticity. Several solutions have been proposed and I trust none of them: they are just too sensitive. If you really want to do something about it, than I you'll really need to do some reading. Since these models are so sensitive, you really need to know what you are doing. A good entry point for that literature is (Williams 2009). But my position is that that problem is basically unsolvable, so not worth worrying about. Hope that helps, Maarten Williams, R. 2009. Using heterogenous choice models to compare logit and probit coefficients across groups. Sociological Methods & Research 37: 531--559. -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: hetroscedasticity test after probit***From:*Yuval Arbel <yuval.arbel@gmail.com>

**References**:**st: hetroscedasticity test after probit***From:*Prakash Singh <prakashbhu@gmail.com>

**Re: st: hetroscedasticity test after probit***From:*Maarten Buis <maartenlbuis@gmail.com>

**Re: st: hetroscedasticity test after probit***From:*Prakash Singh <prakashbhu@gmail.com>

**Re: st: hetroscedasticity test after probit***From:*Muhammad Anees <anees@aneconomist.com>

**Re: st: hetroscedasticity test after probit***From:*Prakash Singh <prakashbhu@gmail.com>

**Re: st: hetroscedasticity test after probit***From:*Muhammad Anees <anees@aneconomist.com>

**Re: st: hetroscedasticity test after probit***From:*Yuval Arbel <yuval.arbel@gmail.com>

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