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

 From Nick Cox To "'statalist@hsphsun2.harvard.edu'" Subject RE: st: Why do -intreg- and -truncreg- not give me the same SD as -summarize- ? Date Tue, 8 Nov 2011 17:11:35 +0000

```Yes, mostly and no, in part, although feel free to call this pedantic.

Using an unbiased estimate of variance does not give you an unbiased estimate of SD, as square rooting is not a linear operation! The bias is usually ignored but it is there.

Nick
n.j.cox@durham.ac.uk

Antoine Terracol

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-.

On 08/11/11 17:11, Richard Williams wrote:
> At 10:02 AM 11/8/2011, Seed, Paul wrote:

>> 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.
>

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