Course Introduction

What’s this course about?

In 200B, we learnt the linear models in the form \[ y = \beta_0 + \beta_1 x_1 + \cdots + \beta_p x_p + \epsilon, \] where
1. \(y\) is a continuous response variable (or dependent variable),
2. \(x_1, \ldots, x_p\) are covariates (or predictors, or independent variables), and
3. \(\epsilon\) is the error term and assumed to be normally distributed and independent among observations.
In 200C, we generalize the linear models in three directions.
1. Generalized linear models (GLMs) handles nonnormal responses, \(y\), such as binary response (disease or not), proportions, or counts.
2. Mixed effects models relaxes the independence assumption of the error term and allows correlation structure in \(\epsilon\).
3. Nonparametric regression models (GAM, trees, neural networks) allow nonlinearity in the effects of predictors \(x\) on responses.

Read syllabus and schedule for a tentative list of topics and course logistics.
Teaching philosophy. Usually a GLM course is taught on blackboard/whiteboard with mostly math derivations. In this course, I will start from R code and then explain the theory behind it.