C20. Logit, probit and odds
How do the logit and probit links differ? Define the odds associated with a success probability p.
Worked answer (click to show)
Definitions/notation. For success probability 0<p<1, odds are p/(1-p), the logit is \log\{p/(1-p)\}, and the probit is \Phi^{-1}(p), where \Phi is the standard normal CDF. These are different links for the same Bernoulli mean p, giving different probability curves and coefficient interpretations.