[R] odds ratio: how to create reference

Eik Vettorazzi E.Vettorazzi at uke.uni-hamburg.de
Tue Sep 23 11:36:30 CEST 2008

```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...
>
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

--
Eik Vettorazzi
Institut für Medizinische Biometrie und Epidemiologie
Universitätsklinikum Hamburg-Eppendorf

Martinistr. 52
20246 Hamburg

T ++49/40/42803-8243
F ++49/40/42803-7790

```