Generalized additive models

Generalized additive models (GAMs) are a non-parametric extension of GLMs in which the linear predictor depends linearly on unknown smooth functions of some predictor variables. GAMs are typically used to let the data "speak for themselves" since you don't need to specify the functional form of the relationship, the response, and the continuous explanatory variables beforehand. To fit your data to a GAM, you will need to obtain the gam() function from the mgcv package. It is similar to the glm() function except that you add s() to each explanatory variable you wish to add smooths. For example, if you wish to describe the relationship between y and to smooth three continuous explanatory variables x, z, and w, you would enter model <- gam(y ~ s(x) + s(z) + s(w)). Now let's go through a detailed example in R.

In this example, we will explore the relationship between the total number of pregnancies and a variety of measurements taken from 300 mice.

Let's first simulate...