Odds Ratio - Role in Logistic Regression

Role in Logistic Regression

Logistic regression is one way to generalize the odds ratio beyond two binary variables. Suppose we have a binary response variable Y and a binary predictor variable X, and in addition we have other predictor variables Z1, ..., Zp that may or may not be binary. If we use multiple logistic regression to regress Y on X, Z1, ..., Zp, then the estimated coefficient for X is related to a conditional odds ratio. Specifically, at the population level

\exp(\beta_x) = \frac{P(Y=1|X=1, Z_1, \ldots, Z_p)/P(Y=0|X=1, Z_1, \ldots, Z_p)}{P(Y=1|X=0, Z_1, \ldots, Z_p)/P(Y=0|X=0, Z_1, \ldots, Z_p)},

so is an estimate of this conditional odds ratio. The interpretation of is as an estimate of the odds ratio between Y and X when the values of Z1, ..., Zp are held fixed.

Read more about this topic:  Odds Ratio

Famous quotes containing the word role:

    “Man, truly the animal that talks, is the only one that needs conversations to propagate its species.... In love conversations play an almost greater role than anything else. Love is the most talkative of all feelings and consists to a great extent completely of talkativeness.”
    —Robert Musil (1880–1942)