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From |
Maarten Buis <[email protected]> |

To |
[email protected] |

Subject |
Re: st: Formally comparing Tobit and Probit estimates |

Date |
Wed, 22 Jan 2014 10:06:44 +0100 |

--- On 21 January 2014 17:11, Radha Shah wrote: >> I am using Stata version 12 for Windows. My question concerns >> formally comparing the coefficients on a Probit and Tobit model. >> >> For the Tobit model I run the following, >> >> tobit y_tobit x1_tobit x2_tobit x3_tobit, ll(0) >> >> where y is either 0 or a positive value. >> >> For the probit model I run the following, >> >> probit y_probit x1_probit x2_probit x3_probit >> >> where y_probit is 0 if y_tobit == 0 and is equal to 1 if y_tobit>0. >> >> Can anyone help me with the coding in Stata to conduct a >> statisitical test to test the hypothesis (for example): x1_tobit = >> x1_probit. >> >> I have seen that I can informally compare the estimates by l >> ooking for sign changes between them or visible differences in >> magnitude between (_b[x1_tobit]/_b[sigma]) and (_b[x1_probit]) >> but I was looking for something more statistically formal. -- On Tue, Jan 21, 2014 at 6:34 PM, Nick Cox answered: > I am assuming that despite your notation the x_1* etc. are really the > same variable(s). > > I can't see that the idea of a formal test makes any sense. > > 1. The coefficients are not even in the same dimensions or units of > measurement. > (It's a pity that statistics courses and texts almost uniformly > neglect such matters.) > > 2. The -tobit- model is linear; the -probit- model is nonlinear. In general, Nick is correct, but as a special case what Radha is looking for can make sense. A Tobit model is linear in the latent dependent variable, but it also implies a probit model on the probability of not being censored. Since in a Tobit model we also have some non-censored observations we can identify the scale of that latent variable, something we cannot do in a probit model. Concretely, this means that we can estimate the error variance (sigma) in a Tobit model, while in a probit model we fix it arbitrarily at 1. So, Radha's idea of comparing (_b[x1]/_b[sigma]) with (_b[x1]) does make sense. Radha could use -suest- to perform such a test. Below is an example: *------------------ begin example ------------------ sysuse auto, clear generate wgt=weight/1000 tobit mpg wgt, ll(17) est store tobit gen byte y = mpg > 17 if mpg < . probit y wgt est store probit suest tobit probit testnl ( [tobit_model]_b[wgt] / [tobit_sigma]_b[_cons] = [probit_y]_b[wgt] ) /// ( [tobit_model]_b[_cons] / [tobit_sigma]_b[_cons] = [probit_y]_b[_cons] ) *------------------- end example ------------------- * (For more on examples I sent to the Statalist see: * http://www.maartenbuis.nl/example_faq ) Hope this helps, Maarten --------------------------------- Maarten L. Buis WZB Reichpietschufer 50 10785 Berlin Germany http://www.maartenbuis.nl --------------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Formally comparing Tobit and Probit estimates***From:*Radha Shah <[email protected]>

**Re: st: Formally comparing Tobit and Probit estimates***From:*Nick Cox <[email protected]>

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