Re: st: Why do -intreg- and -truncreg- not give me the same SD as -summarize- ?

[Antoine Terracol <Antoine.Terracol@univ-paris1.fr>]

Hi,

I'd say this is for the same reason why if you estimate a linear model 
by ML instead of OLS, you'll get a biased estimate of sigma because, as 
William said, ML does not ajust for the number of parameters in the 
degrees of freedom.

Since -truncreg- and -intreg- are estimated using ML, I'm not surprised 
that you get different values for sigma. The "correct" (unbiased) one is 
the one reported by -summarize- and -regress-.

Antoine




On 08/11/11 17:11, Richard Williams wrote:
> At 10:02 AM 11/8/2011, Seed, Paul wrote:
> > Dear all,
> >
> > Here is a puzzle that has been bothering me.
> >
> > Interval regression is designed for the circumstances
> > where an outcome is sometimes observed only to be
> > in a particular range. However it also copes with
> > some (or all) observed values being known exactly.
> > Like -summarize-, -intreg- and -truncreg-
> >
> >
> > But look at this:
> >
> > * Begin program *
> > sysuse auto, clear
> > su price
> > truncreg price ,
> > gen price2 = price
> > intreg price price2
> > * end program *
> >
> > Putting the results together I get:
> > Method | Mean Std. Dev/sigma
> > -------------+---------------------------------
> > summarize | 6165.257 2949.496
> > intreg | 6165.257 2929.499
> > truncreg | 6165.257 2929.499
> >
> > All 3 methods agree on the mean; but we have
> > two different estimates for the standard deviation.
> > The manual does not seem to discuss this.
> > Does anyone know what is going on, and is there any way
> > to correct the SD values from -intreg- & -truncreg-?
>
> I think it has to do with the d.f. and how they are being adjusted for.
> If you do
>
> reg price
>
> you again get the 2949.496, which is the square root of the MST
> (8699525.97). MST is SST/73 = 635065396/73. If you instead use 74 in the
> calculations, you get
>
> . di (635065396/74) ^ .5
> 2929.4991
>
> which is what you are getting with intreg and truncreg. In other words,
> these routines seem to be using N rather than N-1 in their calculations.
>
> I am not sure which SD you consider "correct" but it should just take a
> little algebra to convert from one to the other. The help files or
> manuals probably say something about how the SD is calculated, and why.
>
>
> -------------------------------------------
> Richard Williams, Notre Dame Dept of Sociology
> OFFICE: (574)631-6668, (574)631-6463
> HOME: (574)289-5227
> EMAIL: Richard.A.Williams.5@ND.Edu
> WWW: http://www.nd.edu/~rwilliam
>
> *
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