How Link Functions Extend Linear Regression to Generalized Models
This article explains how the traditional linear regression assumption can be relaxed by using link functions to transform nonlinear outputs into linear responses, enabling more flexible generalized linear models for probabilities and count data.
The previous multiple linear regression model assumes that the dependent variable is modeled as a linear combination of the independent variables.
However, this assumption can be relaxed to fit a more general linear model by introducing a link function that replaces the original formula.
The link function transforms a nonlinear output into a linear response.
There are many possible link functions, for example:
(1) Mapping a response in the range 0 to 1 onto a linear scale, where the response is usually a probability between 0 and 1.
(2) Converting count data into a linear output, where the response variable is the count.
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