What is the purpose of a link function?

By employing LINK functions, we can harness the power of linear models, which inherently make predictions on the entire real number line (-∞ to +∞), while ensuring that the resulting predictions are appropriate and relevant to the context.

For instance, if the outcome variable represents a probability, which naturally ranges from 0 to 1, a link function like the logistic function can be used to transform the linear model's predictions into probabilities, preventing the model from making impossible or meaningless predictions.

Link functions serve as bridges, connecting the ultimate outcome variable to the intricate workings of a linear model. Essentially, they facilitate the translation of a model's parameter estimates for each predictor into a meaningful prediction for the outcome.

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In a linear model, the predictors are combined linearly to form a prediction. However, the raw predictions might extend beyond practical bounds, like predicting values outside the range of the outcome variable. This is where link functions come into play.