Thank you! I have put it at this location: http://czresearch.com/info/goldstein_ratios.pdf <http://czresearch.com/info/goldstein_ratios.pdf>

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From: Droogendyk, Harry [mailto:harry.droogendyk@rbc.com]

Attachments are stripped by the list serve.

-----Original Message----- From: Copeland, Laurel [mailto:Laurel.Copeland@MED.VA.GOV <mailto:Laurel.Copeland@MED.VA.GOV> ] Sent: Thursday, May 13, 2004 1:30 PM To: SAS-L@LISTSERV.UGA.EDU Subject: Re: Dependent variable is ratio of continuous values

Some issues regarding analysis of ratios are addressed in the attached PDF by Richard Goldstein, which I copied from a Univ Virginia Health System site

no longer in existence. -Laurel

On Tue, 11 May 2004 16:35:37 -0400, Talbot Michael Katz <topkatz@MSN.COM> wrote:

>Hi. > >I have a situation where the target variable I want to model takes on >values between 0 and 1, endpoints inclusive, because it is a ratio of >two continuous quantities (e.g., actual sales / sales target)... > >Is there a "preferred" method for modeling ratios of continuous quantities, and if so, is it available in SAS? > > Someone suggested the use of the PROC LOGISTIC events/trials syntax, >but the SAS documentation for that really seems to stress binary >outcome trials... > >Is it legitimate to use PROC LOGISTIC events/trials for continuous >numerator and denominator? > >An econometrics textbook ("Econometric Analysis" by W.H. Greene, 5th >edition, Prentice-Hall) suggests Minimum Chi-Squared Estimation (or >MCSE - - >don't tell Microsoft!) for proportions; it looks like that discussion >was motivated by proportions of binary outcomes, but I think the >equations still work in the case of continuous numerator and >denominator. However, a >search of support.sas.com didn't turn up any procedures that support >the MCSE methodology. One weakness of MCSE is that the estimation only >works when the proportion does not take on the extreme values of 0 or >1. In such cases, it seems that the suggested work-around is to add or subtract a >small constant... > >Is there a SAS procedure that does minimum chi-squared estimation for >proportions? > >I could also transform the ratio from the unit interval to the entire >line with the logit transform, log(y/(1-y)), and then perform a >standard regression. Again, I'd have to smudge the extreme values >before performing the transformation... > >Is it legitimate to logit transform the ratio after slightly modifying >the extreme values, and then do OLS? > >Thanks, as ever, for your indulgence... > >-- TMK --

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