Date:         Sat, 29 Dec 2007 03:51:52 -0800
Reply-To:     dhabtem1 <dhabtem1@GMAIL.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         dhabtem1 <dhabtem1@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

The Tobit model sounds like a good idea at first because by limiting
the predicted values to an upperbound, you're right-censoring your
model.  Unfortunatley, though, if I understand it correctly, a Tobit
model works well with a single upperbound value to right-censor all
your predicted values (eg censoring all predicted values at $5000).
In your case, it sounds like you want a different upperbound for each
predicted value (eg $5000 if the person owes $5000, $2000 if the
person owes $2000, etc.).

I think converting 'dollar amount' to a proportion would indeed work.

Perhaps first begin with a simple scatterplot and overlay it with some
sort of smoothed nonparametric/lowess/local regression curve to get a
feel for the data.  Look carefully at your residuals plots, though--
yet another reason against tobit regression:  it doesn't perform well
under violations of model assumptions (ie non-normally distributed
residuals).