Generalized Linear Models

Generalized Linear Models (GLM or GLZ) are growing in popularity as an alternative to OLS for predictive and explanatory models. They have less restrictive assumptions on the distribution of the dependent variables than an OLS model which allows them to better model a greater variety of real-world problems. Generalized Linear Models are not to be confused with General Linear Models (GLM), which assumes normality and whose family includes OLS and ANOVA.

Often time the assumptions of normality for the dependent variable is too restrictive to model real-world problems.  A classic example is a binary choice model.  A binary choice model estimates the probability of an event happening like whether a person will renew their subscription with a magazine.  To model this type of problem you would use a GLZ with a link function which is also unknown as a logistic regression, which was discussed here: Logistic Models

But GLZs are a useful alternative even when the dependent variable is continuous. For example, insurance claims experience. The severity (or dollar amount) of claims is a continuous variable however the distribution that generates claims experience is not normal. Most polices never report a claims so the bulk of the data is at zero. To make matters worse, the tail of claims experience can be very large. A rare event, like a hurricane over a major metropolitan area can have extreme values ranging in the billions. Below is a graphical example of such a claims loss experience.

GLZ allow for modeling non-normality by using link functions. A link function transforms the dependent variable and models how the dependent variable is related to the independent variable. A GLZ with an Identity link function will yield identical results as a standard OLS with no link function. An Inverse link function would model exponential processes such as acceleration due to gravity. In the claims example you could use a Weibull link function.

Further Reading
StatSoft

Wikipedia

StatSci.org

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