Generalizing Linear Models

We think in generalities, but we live in detail.

- Alfred North Whitehead

In the last chapter, we used a linear combination of input variables to predict the mean of an output variable. We assumed the latter to be distributed as a Gaussian. Using a Gaussian works in many situations, but for many other it could be wiser to choose a different distribution; we already saw an example of this when we replaced the Gaussian distribution with a Student's t-distribution. In this chapter, we will see more examples where it is wise to use distributions other than Gaussian. As we will learn, there is a general motif, or pattern, that can be used to generalize the linear model to many problems.

In this chapter, we will explore:

• Generalized linear models
• Logistic regression and inverse link functions
• Simple logistic regression
• Multiple logistic regression
...