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

[Richard Williams <richardwilliams.ndu@gmail.com>]

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

*
*   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/