Generalized Linear Models and Nonparametric Regression

An Introduction to Generalized Linear Models Through Binomial Regression

In this module, we will introduce generalized linear models (GLMs) through the study of binomial data. In particular, we will motivate the need for GLMs; introduce the binomial regression model, including the most common binomial link functions; correctly interpret the binomial regression model; and consider various methods for assessing the fit and predictive power of the binomial regression model.

Models for Count Data

In this module, we will consider how to model count data. When the response variable is a count of some phenomenon, and when that count is thought to depend on a set of predictors, we can use Poisson regression as a model. We will describe the Poisson regression in some detail and use Poisson regression on real data. Then, we will describe situations in which Poisson regression is not appropriate, and briefly present solutions to those situations.

Introduction to Nonparametric Regression

In this module, we will introduce the concept of a nonparametric regression model. We will contrast this notion with the parametric models that we have studied so far. Then, we’ll study particular nonparametric regression models: kernel estimators and splines. Finally, we will introduce additive models as a blending of parametric and nonparametric methods.

Introduction to Generalized Additive Models

Some models, such as linear regression, are easily interpretable, but inflexible, in that they don't capture many real-world relationships accurately. Other models, such as neural networks, are quite flexible, but very difficult to interpret. Generalized additive models (GAMs) are a nice balance between flexibility and interpretability. In this module, we will further motivate GAMs, learn the basic mathematics of fitting GAMs, and implementing them on simulated and real data in R.