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From |
Michelle <cantibridgian@yahoo.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
RE: st: odds ratio vs. RRR in multinomial logistic regression |

Date |
Fri, 3 Jun 2005 06:16:11 -0700 (PDT) |

Thanks - this is very helpful. One more question: With odds ratios in binary logistic regression, you can easily interpret the exponentiated coefficient by stating that "the odds of outcome 1 are 2.4 times greater than the odds of outcome 2." When I expoentiate the coefficient in multinomial logistic regression (or use the RRR that is provided), I can obviously say "the RRR is .85". But is there some more easily interpretable way that I can describe what this number means, as one could do in binary logistic regression? For instance, can I make a statement about the probability of outcomes 3 as compared to outcome 1? Thanks again. --- David Harrison <david.harrison@icnarc.org> wrote: > It is not quite as bad as you make out... > > You have written the RRR as (using a slightly > shorter shorthand): > > [P(Y=Y2|X)/P(Y=Y1|X)]/[P(Y=Y2|!X)/P(Y=Y1|!X)] > > But, note that you could rearrange this to: > > [P(Y=Y2|X)/P(Y=Y2|!X)]/[P(Y=Y1|X)/P(Y=Y1|!X)] > > This is clearly a ratio of two relative risks - > hence the term relative risk ratio. I don't think it > would be reasonable to refer to the ratio of any two > probabilities as a "relative risk". > > David > > -----Original Message----- > From: n p [mailto:nik_padazis@yahoo.com] > Sent: 03 June 2005 10:13 > To: statalist@hsphsun2.harvard.edu > Subject: Re: st: odds ratio vs. RRR in multinomial > logistic regression > > > Suppose your dependent variable Y has three > categories > : Y1, Y2 and Y3. Let's assume Y1 is used as the > comparison group. Now if you have just one binary > covariate X (0,1) you get two betas from the mlogit > command :b1, b2 > exp(b1)=[P(Y=Y2)/P(Y=Y1) | X=1]/[P(Y=Y2)/P(Y=Y1) | > X=0] > > and exp(b2)=[P(Y=Y3)/P(Y=Y1) | X=1]/[P(Y=Y3)/P(Y=Y1) > | > X=0] > > thus the exponentiated betas are ratios of > probability > > ratios. If one names the probability ratios > "relative > risk" then we get the "relative risk ratios". They > are > not "Odds Ratios" because P(Y=Y2)+P(Y=Y1)!=1 and > similarly P(Y=Y3)+P(Y=Y1)!=1 (whereas in simple > logistic regression P(Y=1)+P(Y=0)=1 thus > P(Y=1)/P(Y=0)= > P(Y=1)/[1-P(Y=1)] that is Odds). > > I hope this is clear and correct > > Nikos Pantazis > Biostatistician > > --- Richard Williams <Richard.A.Williams.5@ND.edu> > wrote: > > > At 08:38 AM 6/2/2005 -0700, Michelle wrote: > > >I understand that mlogit allows you to type "RRR" > > to > > >get the relative risk ratio. My understanding is > > that > > >RRR is the ratio of probabilities, while odds > ratio > > is > > >the ratio of odds. > > >Is this correct? If so, why can't I get an odds > > ratio > > >from mlogit? > > > > Whatever you call it (and different programs call > it > > different things) it > > is the exponentiated coefficient. Different > > programs call it the odds > > ratio, irr, rrr, exp(b). There was a discussion > on > > stata list a little > > while back about what the best terminology was. > > > > ------------------------------------------- > > Richard Williams, Notre Dame Dept of Sociology > > OFFICE: (574)631-6668, (574)631-6463 > > FAX: (574)288-4373 > > HOME: (574)289-5227 > > EMAIL: Richard.A.Williams.5@ND.Edu > > WWW (personal): http://www.nd.edu/~rwilliam > > WWW (department): http://www.nd.edu/~soc > > > > * > > * For searches and help try: > > * > > http://www.stata.com/support/faqs/res/findit.html > > * http://www.stata.com/support/statalist/faq > > * http://www.ats.ucla.edu/stat/stata/ > > > > > __________________________________________________ > Do You Yahoo!? > Tired of spam? Yahoo! Mail has the best spam > protection around > http://mail.yahoo.com > * > * For searches and help try: > * > http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > > > > * > * For searches and help try: > * > http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > __________________________________ Discover Yahoo! Find restaurants, movies, travel and more fun for the weekend. Check it out! http://discover.yahoo.com/weekend.html * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**RE: st: odds ratio vs. RRR in multinomial logistic regression***From:*"David Harrison" <david.harrison@icnarc.org>

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