Logistic Model
A logistic model is a linear regression method for a binary outcome.
Contents
Design
Outcomes are coded as 0 and 1. A linear model is constructed (as x = Xb) to predict outcomes using one or more independent variables.
The intention of the model is to predict the probability of outcome 1. As always, a probability must be a number between 0 and 1. The linear model as specified can produce any number, however. To connect the linear model to expected values, the logistic function is used as a link function.
This function plots as an S-shaped line, so is sometimes called a sigmoid function.
The fitted parameters of this model are in terms of logits or log odds. The logit function is the inverse of the logistic function.
To be clear: logistic(x) = p and logit(p) = x.