Generalised Linear Model — Part 1:

I will try to review and extend more and more this post, in order to show the power and importance of Generalised Linear Model and giving clear practical examples

Generalised Linear Model or GLM are a vast class of models, which try to fit a distribution of points (observations), independently from the distribution function of the observations under study. Such a statement sounds quite strong, but it has remarkable applications from biology to finance, creating a solid foundations for nowadays machine learning world. We often use models derived from GLM in our data science projects (e.g. Linear Regression, Logistic Regression, Poisson Regression), but we spend just very little time to think how everything has started and what is the mathematical background. Furthermore, we tend to define all these models as classification algorithm, while on the paper they are just fitting our data points. In this post I will try to give an introduction of GLM, underlining the most salient features and mathematical aspects.

The foundations

As a first step, we need to assess two main constraints to GLM. Primarly, a generalised linear model is characterised by the independence — or un-correlation — of the observations. As a consequence, data with autocorrelations of time series or spatial processes cannot be fitted using GLMs (e.g. we cannot use our…