# Re: RE : st: tobit?

 From Maarten buis 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

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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