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From |
Maarten buis <[email protected]> |

To |
[email protected] |

Subject |
Re: RE : st: tobit? |

Date |
Tue, 12 Aug 2008 17:25:23 +0100 (BST) |

No, not at all. OLS is remarkably robust for deviations in the distribution of the residuals. I think this is interesting theoretically, but in applied research this would probably be the very last thing I would care about. -- Maarten --- Chris Witte <[email protected]> wrote: > so for the layman... Is the most important measure of fit for a > model the distribution of residuals? > > > > ----- Original Message ---- > From: Stas Kolenikov <[email protected]> > To: [email protected] > Sent: Tuesday, August 12, 2008 10:32:01 AM > Subject: Re: RE : st: tobit? > > The distribution of the standard errors will depend on both the > distribution of the error terms and the distribution of the > explanatory variables (design measure, to wit). But in terms of > working with just the first two moments (means and variances), > nothing > says error must be Gaussian, and the explanatory variables have to be > uniform, to ensure that the estimates are unbiased, and that s^2 > (X'X)^{-1} is an unbiased estimator of variance. In your simulation > example, if you looked at two-sided coverage (and a sample size of > 100), you will probably see that rejections outside the nominal 90% > CI > will be 3% on one side and 12% on the other. > > The distribution of the residuals is closer to normality than that of > the errors. In each residual, all other errors are added up (through > e > = (I-H)errors formula), although with unequal weights. For points of > low leverage, when no such weight dominates too much, some sort of > the > CLT argument will show that the residuals will be approximately > normal. So to see notable non-normality in residuals, you need to > make > quite big departures from normality in errors, and/or points of high > leverage (that would most likely produce small residuals for the > leverage points themselves, but will also skew the distribution of > all > other terms a little bit). > > On Tue, Aug 12, 2008 at 10:17 AM, Maarten buis > <[email protected]> wrote: > > --- Gaul� Patrick <[email protected]> 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/ > > > > > > -- > Stas Kolenikov, also found at http://stas.kolenikov.name > Small print: I use this email account for mailing lists only. > > * > * 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/ > > > > > > * > * 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/ > ----------------------------------------- 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/

**References**:**Re: RE : st: tobit?***From:*Chris Witte <[email protected]>

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