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


From   "Seed, Paul" <paul.seed@kcl.ac.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Why do -intreg- and -truncreg- not give me the same SD as -summarize- ?
Date   Wed, 9 Nov 2011 10:20:29 +0000

Thank you very much Richard.  That is very helpful.
As I generally use SST/(N-1) for the variance, 
I will do so in future when I have to summaize censored data.

Best wishes, 
Paul T Seed, Senior Lecturer in Medical Statistics, 
Division of Women's Health, King's College London
Women's Health Academic Centre KHP
020 7188 3642.
"I see no reason to address the comments of your anonymous expert 
... I prefer to publish the paper elsewhere" - Albert Einstein



Date: Tue, 08 Nov 2011 11:11:22 -0500
From: Richard Williams <richardwilliams.ndu@gmail.com>
Subject: Re: st: Why do -intreg- and -truncreg- not give me the same SD as -summarize- ?
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.
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