Date:         Wed, 2 Jan 2008 12:28:31 -0500
Reply-To:     Wensui Liu <liuwensui@GMAIL.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Wensui Liu <liuwensui@GMAIL.COM>
Subject:      Re: Regression where dependent variable has an upperbound
Comments: To: Xu Zeng <xuzeng@hotmail.com>
In-Reply-To:  <200712281510.lBSBkNUu014912@mailgw.cc.uga.edu>
Content-Type: text/plain; charset=ISO-8859-1

Xu,
For your problem, I would use a 2-stage estimation method.
1) estimate predicted collection Yhat conditional on X but
unconditional on Yhat <= Y
2) after getting Yhat, estimate predicted probability Yhat <= Y conditional on X
3) so the expected Yhat conditional on Yhat <= Y should be Yhat *
Prob(Yhat <= Y)

Just my $0.02.

On Dec 28, 2007 10:10 AM, Xu Zeng <xuzeng@hotmail.com> wrote:
> I am trying to predict dollar amount collected for people who have various
> debts. But this dependent variable can never exceed the original amount of
> debt people owe. For example, if someone owes $5000 then the predicted
> collected $ must be <=5000 (I am not considering interests for simplicity).
>
> I will definitely use the original owed amount as one of independent
> variabls and the coefficient of it will be less than 1 (in a linear
> regression). But I will probably have many other variables, I can't 100%
> sure that the predicted amount will be less than original debt amount. Of
> course, I can adjust the prediction at the end, but I would like to know if
> there is a SAS regression procedure or statistical method that will
> guarantee the prediction never exceeds the upperbound.
>
> Your advice and suggestion will be greatly appreciated.
>
> Thank you very much and happy new year.
>



--
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WenSui Liu
Statistical Project Manager
ChoicePoint Precision Marketing
(http://spaces.msn.com/statcompute/blog)
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