Logit Model and Odds Ratio. Dan Saunders. Since logit is a binary response
model, it is natural to think of the dependent variable in the logit model as a ...
Logit Model and Odds Ratio Dan Saunders Since logit is a binary response model, it is natural to think of the dependent variable in the logit model as a bernoulli random variable: 1 with probability = p yi = 0 with probability = 1 − p Odds are defined as the ratio of these two probabilities: p 1−p The Logit regression model is defined by the equation: p logit(p) ≡ ln = x0i β + i 1−p Normally, the coefficients Stata reports are the coefficent vector β. The odds ratio is calculated as exp(β), since p p exp ln = exp(x0i β + i ) = 1−p 1−p 0 p p exp(x0i β + βj + i ) = exp(βj ) ⇒ / = 1 − p0 1−p exp(x0i β + i ) It can be thought of as the fraction with numerator (the odds of y after a 1 unit increase in x) and denominator (the odds of y before x is increased by 1 unit). Therefore we are measuring the relative change in the odds of the response variable y for a 1 unit increase in regressor j. If the odds ratio is bigger than 1, then the underlying probability, p, that y = 1 has increased. It is actually possible to back out the underlying probabilities and the changes in probabilities. For any predicted odds ratio we have ey =
