The logistic model

We have almost all the elements to turn a simple linear regression into a simple logistic regression. Let's begin with the case of only two classes or instances, for example ham/spam, safe/unsafe, cloudy/sunny, healthy/ill, or hotdog/not hotdog. First, we codify these classes by saying that the predicted variable, , can only take two values, 0 or 1, that is, . Stated this way, the problem sounds similar to the coin-flipping example from Chapter 2, Programming Probabilistically and Chapter 3, Modeling with Linear Regression.

We may remember we used the Bernoulli distribution as the likelihood. The difference with the coin-flipping problem is that now is not going to be generated from a beta distribution; instead, is going to be defined by a linear model with the logistic as the inverse link function. Omitting the priors we have:

Notice that the main difference with the simple linear regression from Chapter 3, Modeling with Linear Regression is the use of a Bernoulli distribution instead of a Gaussian distribution, and the use of the logistic function instead of the identity function.

Table of Contents for The logistic model

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Table of Contents for
The logistic model