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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: RE : st: tobit? |

Date |
Tue, 12 Aug 2008 16:17:44 +0100 (BST) |

--- Gaulé Patrick <patrick.gaule@epfl.ch> wrote: > >You should be careful however that > >the assumption behind -regress- is not that BMI is normally > >distributed, but that the residuals are normally distributed. > > My understanding is that the desirable properties of ordinary least > squares hold without the normality assumption. Moreover, the > assumption would be that the error term, not the residuals, is > normally distributed. -regress- will always give you the line/(hyper)plane that minimizes the sum of squared errors, regardless of the distrubtion of the error term. In that sense you are correct. I have always learned that the standard errors depend on the distribution of the error term. However, when I simulated this with a skewed error term (log-normal with mean zero), the p values seem ok: approximately uniformly distributed and approximately 500 rejections of the true null hypothesis out of 10,000 draws. Regarding your second comment: The distribution of the residuals gives you an estimate of the distribution of the error term. -- Maarten *-------------------- begin simulation ------------------------- capture program drop sim program sim, rclass drop _all set obs 1000 gen x = invnorm(uniform()) gen y = 1 + x + exp(invnormal(uniform())) - exp(.5) reg y x tempname t scalar `t' = (_b[x]-1)/_se[x] return scalar p = 2*ttail(`e(df_r)', abs(`t')) end simulate p=r(p), reps(10000) : sim hist p count if p < .05 *----------------------- end simulation ------------------------ ----------------------------------------- Maarten L. Buis Department of Social Research Methodology Vrije Universiteit Amsterdam Boelelaan 1081 1081 HV Amsterdam The Netherlands visiting address: Buitenveldertselaan 3 (Metropolitan), room Z434 +31 20 5986715 http://home.fsw.vu.nl/m.buis/ ----------------------------------------- Send instant messages to your online friends http://uk.messenger.yahoo.com * * 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: RE : st: tobit?***From:*"Stas Kolenikov" <skolenik@gmail.com>

**References**:**RE : st: tobit?***From:*Gaulé Patrick <patrick.gaule@epfl.ch>

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