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From |
Yuval Arbel <[email protected]> |

To |
[email protected] |

Subject |
Re: st: hetroscedasticity test after probit |

Date |
Thu, 5 Jul 2012 12:27:33 +0300 |

Maarten, I believe your implication refers to specification errors in the model, i.e., omission of relevant explanatory variables, leading to biased and inconsistent estimates and predictions. Am I correct? On Thu, Jul 5, 2012 at 11:56 AM, Maarten Buis <[email protected]> wrote: > 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/ -- Dr. Yuval Arbel School of Business Carmel Academic Center 4 Shaar Palmer Street, Haifa 33031, Israel e-mail1: [email protected] e-mail2: [email protected] * * 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:*Maarten Buis <[email protected]>

**References**:**st: hetroscedasticity test after probit***From:*Prakash Singh <[email protected]>

**Re: st: hetroscedasticity test after probit***From:*Maarten Buis <[email protected]>

**Re: st: hetroscedasticity test after probit***From:*Prakash Singh <[email protected]>

**Re: st: hetroscedasticity test after probit***From:*Muhammad Anees <[email protected]>

**Re: st: hetroscedasticity test after probit***From:*Prakash Singh <[email protected]>

**Re: st: hetroscedasticity test after probit***From:*Muhammad Anees <[email protected]>

**Re: st: hetroscedasticity test after probit***From:*Yuval Arbel <[email protected]>

**Re: st: hetroscedasticity test after probit***From:*Maarten Buis <[email protected]>

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