Logistic regression: Difference between revisions

Revision as of 18:26, 6 June 2006

Revision as of 15:44, 7 June 2006

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The logarithm of the [[odds]] (probability divided by one minus the probability) of the outcome is modelled as a linear function of the explanatory variables, ''X''₁ to ''X''_''k''. This can be written equivalently as

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