5. GAMs

Generalized additive models (GAMs) are extensions of the generalized linear models (GLMs) we discussed in earlier chapters. Like GLMs, GAMs accommodate outcomes that are both continuous and discrete. However, unlike GLMs that are fully parametric models, GAMs are semi-parametric models. GAMs allow a mix of a parametric and a nonparametric association between outcome and predictors. For this chapter, we will lean heavily on one excellent R package, VGAM, which provides utilities for vector generalized linear models (VGLMs) and vector generalized additive models (VGAMs) [125]. VGAMs are an even more flexible class of models than GAMs where there may be multiple responses. However, beyond offering flexibility of multiple parameters, the VGAM package implements over 20 link functions, well over 50 different models/assumed distributions. We will only scratch the surface of the VGAM package capabilities in this chapter, but its great flexibility means that we will not need to introduce many different packages nor many different functions. If you would like to learn about VGAMs in far greater depth, we recommend an excellent book by the author of the VGAM package [125].

                library(checkpoint)
                checkpoint("2018-09-28", R.version = "3.5.1",
                  project = book_directory,
                  checkpointLocation = checkpoint_directory,
                  scanForPackages = FALSE,
                  scan.rnw.with.knitr = TRUE, use.knitr = TRUE)
               
                library(knitr)
                library(data.table)
                library(ggplot2)
                library(ggthemes)
                library(scales)
                library(viridis)
                library(car)
                library(mgcv)
                library(VGAM)
                library(ipw)
                library(JWileymisc)
                library(xtable)
               
                options(
                  width = 70,
                  stringsAsFactors = FALSE,
                  datatable.print.nrows = 20,
                  datatable.print.topn = 3,
                  digits = 2)