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


From   "David Harrison" <david.harrison@icnarc.org>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: odds ratio vs. RRR in multinomial logistic regression
Date   Fri, 3 Jun 2005 10:34:58 +0100

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
> 
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