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 words role in and/or role:

    “Always and everywhere children take an active role in the construction and acquisition of learning and understanding. To learn is a satisfying experience, but also, as the psychologist Nelson Goodman tells us, to understand is to experience desire, drama, and conquest.”
    —Carolyn Edwards (20th century)

    “Is not our role to stand for the one thing which means our own salvation here but with which it will also be possible to save the world, and with which Europe will be able to save itself, namely the preservation of the white man and his state?”
    —Hendrik Verwoerd (1901–1966)