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:

    “My role in society, or any artist or poet’s role, is to try and express what we all feel. Not to tell people how to feel. Not as a preacher, not as a leader, but as a reflection of us all.”
    —John Lennon (1940–1980)

    “Scholars who become politicians are usually assigned the comic role of having to be the good conscience of state policy.”
    —Friedrich Nietzsche (1844–1900)