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

 From Michelle <[email protected]> To [email protected] 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 <[email protected]> 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:[email protected]]
> Sent: 03 June 2005 10:13
> To: [email protected]
> 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 <[email protected]>
> 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:  [email protected]
> > WWW (personal):    http://www.nd.edu/~rwilliam
> > WWW (department):    http://www.nd.edu/~soc
> >
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