[R] odds ratio: how to create reference

Eik Vettorazzi
2008-09-23T09:36:30Z

Hi,
You can state a probability p as odds p/(1-p) and vice versa. To get an
odds ratio you need actually two odds. Then you can get the odds ration
of being/having "a" instead of "b" by odds(a)/odds(b), where
"b" is the
reference level.
If you fit a logistic regression model (which means that your outcome is
dichotomous) then the estimated coefficients are actually
log(oddsratios) - which you can transform to odds by exp() .
You can use a factor-variable with three levels for race and
treatment-contrasts to get odds ratios for not being white against being
white - make sure, that either your factor has "white" as first level
or
specify the contrast with the "base" argument.
If you create 3 dummy variables and involve an intercept in your model
your model will be perfectly collinear - the so called "dummy variable
trap" - you can use an intercept and create two dummies for the
covariate levels you are actually interested in and put this in your
logistic model - the result will be the same as with the treatment
contrasts.

hth.

Bunny, lautloscrew.com schrieb:
> HI there,
>
> i know this is a basic question, though i need some help because this
> is somewhat away from my current issue, but nevertheless interesting
> to me... Lets assume i have some estimated probabilities, say
> estimated by a logit model. i know i can also state them as an odds
> ratio.
>
> Now i?d like to state these odds ratios as a reference to a specific
> outcome of my investigated variable.
>
> for example, if my covariate of interest is race and possible outcomes
> are white, black and hispanic, whereas the latter are minorities in my
> case - how can i state the odds ratio in such a way that white is the
> reference (always 1) and other races' odds ratio are relative to the
> reference. e.g. hispanics are 1.5 times more likely to ...
>
> Is creating 3 binary dummies for race the right way  ? And if so how
> can i go on.
> As i said, i know this is rather basic, i am thankful for any links /
> references...
>
> thanks in advance !
>
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--
Eik Vettorazzi
Institut f?r Medizinische Biometrie und Epidemiologie
Universit?tsklinikum Hamburg-Eppendorf

Martinistr. 52
20246 Hamburg

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