```Date: Fri, 14 Jan 2011 08:56:09 -0500 Reply-To: Peter Flom Sender: "SAS(r) Discussion" From: Peter Flom Subject: Re: Mutlinomial Logit to Binomial Logit.. Comments: To: Tanmoy Mukherjee Content-Type: text/plain; charset=UTF-8 My comments interspersed Tanmoy Mukherjee 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 ```

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