13.15 Nonlinear regressions

• not accounting for non-linearity messes up results: range, slope

• usually tailored to dependent variable
• binary dependent variables: usually OLS nontheless, but called linear probability model (LPM)
• one way: generalized linear model (GLM): $Y = F(\beta_0 + \beta_1X)$, where $F$ is the link function and the inside the index.

13.15.1 good link functions

• take any value from $-\infty$ to $\infty$
• output values between 0 and 1
• input increases –> output increases
• popular functions: logit, probit

13.15.2 Interpretation

• use marginal effects
• $\frac{\partial Pr(Y = 1)}{\partial X} = \beta_1 Pr(Y = 1) (1- Pr(Y = 1))$
• but this changes with every $X$
• recommendation against marginal effect at the mean
• instead: average marginal effect