Date:         Tue, 1 Jan 2008 04:59:28 -0800
Reply-To:     JianAn Lu <loginon@GMAIL.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         JianAn Lu <loginon@GMAIL.COM>
Organization: http://groups.google.com
Subject:      Re: Regression where dependent variable has an upperbound
Comments: To: sas-l@uga.edu
Content-Type: text/plain; charset=ISO-8859-1

On Jan 1, 5:10 am, liuwen...@GMAIL.COM (Wensui Liu) wrote:
> Mary,
> for the simplest case, what i learned from stat101 is that
> yhat = y|x = x'b, where y = yhat + e and e ~ normal() such that E(e) = 0
>
> however, per your sas code in the email, the my takehome message is that
> y = yhat + max(e, 0)
> which i don't know how to solve it mathematically.
>
> just my $0.02.
>
> On Dec 31, 2007 3:11 PM, Mary <mlhow...@avalon.net> wrote:
>
>
>
>
>
> > Xu Zeng,
>
> > Is it really necessary to do this within the logistic regression procedure?  Why couldn't you save the predicted values, merge them to the actual values, and then in a data step adjust any values that are over the owed amount to the owed amount, like this?
>
> > data new;
> > /* merge {predicted and actual } */
>
> > if predicted_owed_amount > actual_owed_amount then
> >   do;
> >       predicted_owed_amount=actual_owed_amount;
> >   end;
>
> > -Mary
> >   ----- Original Message -----
> >   From: Xu Zeng
> >   To: SA...@LISTSERV.UGA.EDU
> >   Sent: Friday, December 28, 2007 9:10 AM
> >   Subject: Regression where dependent variable has an upperbound
>
> >   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.
>
> --
> ===============================
> WenSui Liu
> Statistical Project Manager
> ChoicePoint Precision Marketing
> (http://spaces.msn.com/statcompute/blog)
> ===============================- Hide quoted text -
>
> - Show quoted text -

How about regression on the odds of expected lost: log(expected lost/
(bad debt-expected lost))?