**Date:** Fri, 14 Jan 2011 08:56:09 -0500
**Reply-To:** Peter Flom <peterflomconsulting@mindspring.com>
**Sender:** "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
**From:** Peter Flom <peterflomconsulting@MINDSPRING.COM>
**Subject:** Re: Mutlinomial Logit to Binomial Logit..
**Content-Type:** text/plain; charset=UTF-8
My comments interspersed

Tanmoy Mukherjee <tkmcornell@YAHOO.COM> wrote
>
>I have a question regarding transforming the Multinomial Logit to a Bionomial Logit. I know this is not >the right way to do so but the reason for doing so was that it is more transparent and convenient to do a >Binary estimation than a Multinomial estimation. I am not too comfortable with the Multinomial model and >therefore adopted the Binomial approach.
>

OK. I could suggest becoming comfortable with the multinomial approach. I have a paper on this at NESUG, available here:

http://www.statisticalanalysisconsulting.com/multinomial-and-ordinal-logistic-regression-using-proc-logistic-2/

or via Lex Jansen's site, but for now, OK

>My data is of the form where there are three outcomes C2D, C2P and C2C.

I think you mean that the response has 3 levels. That is, there is ONE dependent variable, but it has three possible levels. Are these ordered or unordered?

>C2C is the outcome with the >highest events and therefore is the residual.

I believe you mean "therefore is the reference level". This is a common approach, but I can't recommend it as a universal rule; it depends on what these outcomes ARE. There may be one response that is "normal" and two that are not; or there may be other reasons to call one the reference level.

>MULTINOMIAL MODEL APPROACH
>We can estimate the odds ratio or the probabilities using a Multinomial Logit where C2C =1, C2D =2 and >C2P=3. Since C2C is the event with the highest occurrence we will use it as the reference. This will give >us the odds ratios from where we can compute the conditional probabilities of Pr(C2D)/Pr(C2C) and >Pr(C2P)/Pr(C2C). Rearranging the equations we can get the individual probabilities of Pr(C2P) and Pr(C2D) >and the Pr(C2C) = 1- (Pr(C2D) - Pr(C2P).
>

Ummmm, OK. But you can also have SAS do this for you. See my paper, above

>Now if we were to estimate the same probabilities using Binomial Logits, question is how will we go about >doing this?
>
>SELF-BINOMIAL APPROACH
>The approach I used was as follows :
>
>Break the data into two sets where :
>
>a) Set I : Describe events as C2D=1 and (not C2D)=0; Calculate the odds ratio and the Pr(C2D) through this
>b) Set II: Describe events as C2P=1 and (not C2P)=0; Calculate the odds ratio and the Pr(C2P) through this
>
>and then compute Pr(C2C) = 1- Pr(C2D) - Pr(C2P)
>
>However, problem I am getting is that sometimes Pr(C2D) + Pr(C2P) > 1 and that creates a problem.
>
>ONLINE DESCRIBED BINOMIAL APPROACH
>I looked up online and it seems the correct approach should have been :
>
>a) Set I : Data with only two outcomes C2D and C2C; Reject data where C2P
>b) Set II: Data with only two outcomes C2P and C2C; Reject data where C2D
>
>This will give you the odds ratio from where we can compute the probabilities i.e. from (a) Pr(C2D)/Pr(C2C) and b) Pr(C2P)/Pr(C2C) and then you can calculate to get the individual probabilities
>Pr(C2P) Pr(C2D) and Pr(C2C)=1-Pr(C2P) - Pr(C2D).
>
>I will appreciate if you can help me with the same.
>

The online approach is correct. It is easy to do this in SAS, using a WHERE statement.

That is, for the first set, do regular PROC LOGISTIC and add

WHERE DV = 'C2D' OR DV = 'C2C';

HTH

Peter

Peter L. Flom, PhD
Statistical Consultant
Website: http://www DOT statisticalanalysisconsulting DOT com/
Writing; http://www.associatedcontent.com/user/582880/peter_flom.html
Twitter: @peterflom