Regression: binary logistic
Simple and multiple linear regression models study the relationship between a single continuous dependent variable Y and one or multiple independent variables X, respectively, using the logistic model and the probit model.
Abstract
Simple and multiple linear regression models study the relationship between a single continuous dependent variable Y and one or multiple independent variables X, respectively (Bangdiwala, 2018a, 2018b). If the value of the dependent variable Y can be only one of two outcomes (i.e. a binary variable, such as dead/alive, injured/not injured, or crash/no crash), the linear predictor function Xb (which equals b0 þ b1X1 þ b2X2 when we have two independent variables X1 and X2) would need to map onto the two values. Typically we consider the dependent variable Y as an indicator variable and assign the value of 1 to the outcome one is trying to predict, and the value of 0 to the other outcome. Mapping a linear predictor to only two values is not possible, so we have it map to the range of values from 0 to 1. Since probabilities range from 0 to 1, we map the linear predictor to a probability. Two common methods are the logistic model and the probit model. In the logistic model, we assume that the probability of Y having the value of 1 is given by the inverse of the log-odds or logit function: