How to build a GLM?

Generalized Linear Models in Python

Ita Cirovic Donev

Data Science Consultant

Components of the GLM

Formula representation for the random component

Formula representation for the random and systematic component

Formula representation for the random and systematic component with the illustration of the interaction effect.

Formula representation for the random and systematic component with the illustration of the interaction and curvilinear effect.

Formula representation for the random and systematic component and the link function

Distribution plot of the continuous random variable.

Data type: continuous
Domain: $(-\infty,\infty)$
Examples: house price, salary, person's height

Family: Gaussian()
Link: identity
$g(\mu) = \mu = E(y)$

Model = Linear regression

Distribution plot of the binary random variable.

Data type: binary
Domain: $0,1$
Examples: True/False

Family: Binomial()
Link: logit

Model = Logistic regression

Distribution plot of the count data.

Data type: count
Domain: $0, 1, 2, ..., \infty$
Examples: number of votes, number of hurricanes

Family: Poisson()
Link: logarithm

Model = Poisson regression

Density	Link: $\eta=g(\mu)$	Default link	`glm(family=...)`
Normal	$\eta = \mu$	identity	`Gaussian()`
Poisson	$\eta = log(\mu)$	logarithm	`Poisson()`
Binomial	$\eta = log[p/(1-p)]$	logit	`Binomial()`
Gamma	$\eta = 1/\mu$	inverse	`Gamma()`
Inverse Gaussian	$\eta = 1/\mu^2$	inverse squared	`InverseGaussian()`

A unified framework for many different data distributions
- Exponential family of distributions
Link function
- Transforms the expected value of y
- Enables linear combinations
- Many techniques from linear models apply to GLMs as well

Generalized Linear Models in Python