Chapter 15Regression for Binary and Count Data
There are 10 types of people in the world, those who can read binary, and those who can't.
– Anonymous
15.1 Introduction
Traditional simple or multiple linear regression assumes a normally distributed response centered at a linear combination of the predictors. For example, in simple regression, the response yi is modeled as normal
, where the expectation, conditional on covariate xi, is a linear function of xi.
For some regression scenarios this model is inadequate because the response is not normally distributed. The response could be categorical, for example, with two or more categories (“disease present–disease absent,” “survived–died,” “low–medium–high,” etc.) or be integer valued (“number with the disease,” “number of failures,” etc.), and yet a response may still depend on a covariate or a vector of covariates, x. In this chapter we discuss logistic and Poisson regressions that are appropriate models for binary and counting responses.
In logistic ...
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