6  Generalised Linear Models (GLM)

6.1 Logistic Regression

A logistic regression model is used when the dependent variable is binary (e.g., 0 or 1, yes or no). The logistic regression model is expressed as:

\log\left(\frac{p}{1-p}\right) = \alpha + \beta_1 X_{i1} + \beta_2 X_{i2} + \ldots + \beta_k X_{ik} \tag{6.1}

Where:

  • p is the probability of the dependent variable being 1,
  • X_{i1}, X_{i2}, \ldots, X_{ik} are the k predictor variables for the i-th observation,
  • \alpha is the intercept,
  • \beta_1, \beta_2, \ldots, \beta_k are the coefficients for the k predictor variables.