Logistic regression: Difference between revisions

Revision as of 16:13, 25 April 2006

Revision as of 17:19, 25 April 2006

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:<math>p = \Pr(Y_i = 1|X) = \frac{\exp(\alpha + \beta_1 x_{1,i} + \cdots + \beta_k x_{k,i})}{1+\exp(\alpha + \beta_1 x_{1,i} + \cdots + \beta_k x_{k,i})}.</math>

The interpretation of the <math>\beta</math> parameter estimates is as a multiplicative effect on the the odds ratio. In the case of a dichotomous explanatory variable, for instance sex, <math>e^\beta</math> (the antilog of <math>\beta</math>) is the estimate of the [[odds-ratio]] of having the outcome for, say, males compared with females.

The parameters &alpha; &beta;₁, ..., &beta;_''k'' are usually estimated by [[maximum likelihood]].