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

 From Antoine Terracol To statalist@hsphsun2.harvard.edu Subject Re: st: Why do -intreg- and -truncreg- not give me the same SD as -summarize- ? Date Tue, 08 Nov 2011 17:59:31 +0100

```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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```
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