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# RE: st: right censoring of dependent and independent variable

 From Garry Anderson To statalist@hsphsun2.harvard.edu Subject RE: st: right censoring of dependent and independent variable Date Fri, 30 May 2008 18:52:29 +1000

```I was using fractional polynomials and so non-linearities are likely. It
seems unfortunate that observations of predictors with right censored
values need to be deleted from the analysis because I would think there
is at least some information in the censored value.

Best wishes, Garry

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten buis
Sent: Thursday, May 29, 2008 10:44 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: right censoring of dependent and independent variable

--- Garry Anderson <g.anderson@unimelb.edu.au> wrote:
> I have data where both the dependent and independent variable are
> right censored and continuous. Although intreg, cnreg or tobit can
> handle censoring of the dependent variable, they do not seem to allow
> censoring of the independent variable. Both the instruments can only
> measure to a maximum value, 30% of values are right censored on the Y
> variable and 15% on the X variable.
>
> I would welcome suggestions as to how to incorporate right censoring
> of the independent variable?

In the graph below you can see that selection on the x variable is much
less of a problem than selection on the y variable. A part of the data
is turned into influential outliers, by selecting on the y. In the
example it is the upper right part of the observed values that pull the
regression line down. However, the same does not happen when you select
on x. With regression you model the mean of y conditional on x, the fact
that you don't observe all values of x, is unfortunate (loss of
power) but not disastrous. Things become obviously more complicated when
you are interested in any non-linearities in the effect of x.

Hope this helps,
Maarten

*----------------------- begin example ------------------------ clear
set seed 12345 matrix C = (1, .5 \ .5, 1) drawnorm x y, n(1000) corr(C)
twoway scatter y x if x < 1, aspect(1) xline(1) || ///
scatter y x if x >= 1, msymbol(oh) mcolor(gs10) || ///
lfit y x , lpattern(solid) lcolor(green) || ///
lfit y x if x < 1, lpattern(solid) lcolor(red) ///
title(selection on x) name(x, replace) ///
legend(order( 1 "observed" ///
2 "censored" ///
3 "true"     ///
4 "estimated") ///
rows(2))

twoway scatter y x if y < 1, aspect(1) yline(1) || ///
scatter y x if y >= 1, msymbol(oh) mcolor(gs10) || ///
lfit y x , lpattern(solid) lcolor(green) || ///
lfit y x if y < 1, lpattern(solid) lcolor(red) ///
title(selection on y) name(y, replace) ///
legend(order( 1 "observed" ///
2 "censored" ///
3 "true"     ///
4 "estimated") ///
rows(2) colfirst)

grc1leg y x
*------------------------ end example --------------------------- (For
more on how to use examples I sent to the Statalist, see
http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html )

For this example to run you need to download the -grc1leg- package,
see: -findit grc1leg-.

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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```

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