st: RE: how to deal with a censored and skewed regressor?

[Steven Samuels <sjhsamuels@earthlink.net>]

There is a literature on censored regressors.  A quick Google search  
on "censored regressors" turned up, for example:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1071239
http://web.mit.edu/tstoker/www/research.htm

The original poster has not yet responded to Al Feiveson, so we do  
not know whether the regressor "x", say, is "censored" in the  
technical sense (has unobserved values <0 that are coded as zero). If  
there are many zeros, perhaps x was generated by one of two  
processes: the first for whether x would be non-zero, the second for  
the value of x if it were non-zero.

One way to handle a mixture would be to generate two variables, an  
indicator that x is zero and, for non-zero x, the actual value.

x_zero = x ==0 & x<.
x_pos  = x*(x > 0 & x<.)   or xlog_pos = log(x)*(x > 0 & x<.)

Insert x_zero and either x_pos or xlog_pos into the predictor list.   
In fact, it is not necessary to choose between logged and unlogged  
versions; -fracpoly-  could model the best transformation of x_pos.

The references above suggest that the indicator approach is biased if  
x is truly censored.

-Steve

On Jan 8, 2009, at 11:29 AM, Lachenbruch, Peter wrote:

> Since the goal is to look at a logarithmic relationship, I'm wondering
> if using glm with a log-link for a normal family wouldn't be helpful.
> That way you don't need to worry about 0 values.
>
> Tony
>
> Peter A. Lachenbruch
> Department of Public Health
> Oregon State University
> Corvallis, OR 97330
> Phone: 541-737-3832
> FAX: 541-737-4001
>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Feiveson,
> Alan H. (JSC-SK311)
> Sent: Wednesday, January 07, 2009 11:54 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: RE: RE: RE: how to deal with a censored and skewed
> regressor?
>
> If there were other X-variables, one way (probably not the best) would
> be to use multiple imputation. More generally, some sort of structural
> model that relates Y to true X and includes the censoring mechanism
> could be estimated (ha!). I suspect there are econometric models out
> there that do this sort of thing - possibly even already programmed in
> Stata.
>
> AL F.
>
>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
> Sent: Wednesday, January 07, 2009 1:06 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: RE: RE: how to deal with a censored and skewed
> regressor?
>
> And how would you do that? Other than knowing that c.i.s and P-values
> are not as good as they seem, what difference does this knowledge make
> to what you do?
>
> Nick
> n.j.cox@durham.ac.uk
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Feiveson,
> Alan H. (JSC-SK311)
> Sent: 07 January 2009 18:27
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: RE: how to deal with a censored and skewed regressor?
>
> Nick wrote: "If you regard such a regressor as error-free, as one
> usually does, then I am not clear that procedure need otherwise be
> affected."
>
> But if the variable (say X )is censored, then it's real value is  
> unknown
> except for an upper or lower bound and there is error ,hence bias  
> in the
> regression parameter estimates if X is used as is. So in mbaier's  
> case,
> if X is really censored at zero, that means it's true value is some
> negative number. This needs to be taken into account in the  
> estimation.
>
> Al Feiveson
>
>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
> Sent: Wednesday, January 07, 2009 12:09 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: how to deal with a censored and skewed regressor?
>
> (x - r(min)) / (r(max) - r(min))
>
> does not yield missing when r(min) is 0 unless x is missing or r 
> (max) is
> also zero. But that's neither here or there. The above is just a  
> linear
> rescaling of a variable and will thus leave skewness unchanged.
>
> Skewness of a regressor is not itself fatal to anything.
>
> Censoring of a regressor is something to take account of in
> interpretation. If you regard such a regressor as error-free, as one
> usually does, then I am not clear that procedure need otherwise be
> affected.
>
> Nick
> n.j.cox@durham.ac.uk
>
> mbaier
>
> I tried to transform it according to ln(skewed variable), but my
> regressor has a lots of values at zero, for which ln is not defined. I
> also tried to create an index like I=100*(x-r(min))/(r(max)-r(min)),
> which again leads to many missings (due to many x's being zero).
> What can I do?
> Besides, do I have to account for the censoring of my regressor? If  
> so,
> what can I do?
> w.ats.ucla.edu/stat/stata/

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