What is the purpose of the logit link function in logistic regression?

The logit link function in logistic regression is primarily used to facilitate model interpretation. It transforms the linear combination of independent variables into a probability value that can be interpreted directly as the likelihood of the dependent variable belonging to a particular category (typically a binary outcome).

By applying the logit function, which is defined as the natural logarithm of the odds (the ratio of the probability of success to the probability of failure), it allows for a clearer interpretation of how changes in predictor variables influence the odds of the outcome occurring. This becomes especially useful for understanding the strength and direction of the relationship between the predictors and the outcome.

Interpreting the coefficients of the logistic regression model becomes more intuitive when considering the exponential form of those coefficients, which provide insights into how a one-unit increase in a predictor affects the odds of the outcome. Thus, the logit link function is essential for translating the outputs of the model into meaningful insights for decision-making and communication of results.