Extending linear models
When to trust it, and how to fix it when it’s broken
Objective
Here we will consider the robustness of linear models to broken assumption. We will also extend the model to account for assumptions. This module should be seen as a brief introduction to other techniques; many of these approaches could be the focus of upper-level classes.
By the end of the lesson, students should be able to
- explain when linear models can be used despite broken assumptions
- extend linear models using
- data transformations
- generalized linear models
- non-linear models
- random effects
- weighted least squares
Background reading
Course notes links for background reading also contain code used to produce R output used in slides.
Lecture slides (click to open in Google slides!)
Connected assignment(click here)
Using these skills and applying concepts correctly to interpret data sets may seem easy when you read about them or listen during class, but practice is key to ensuring you understand the material. Practice problems are provided for each lesson. The link above points you to the appropriate link in the course notes. You can make a copy (technically a fork, since you can’t directly edit it) of the entire course notes website in github @ https://github.com/jsgosnell/cuny_biostats_book and work from there. The benefit is this allows you to see updates to the site (if you sync your fork). The downside is you have to work interactively or build the entire site when you render a changed file. This is doable but may take more time than students need (and may lead to merge issues!).
Alternatively,your instructor may use a different delivery method (like github classroom) or provide alternative problems.
In general you should only work edit .qmd files! Everything/anything else is produced during the session and should not be edited. All files can be uploaded to github though.
Solutions are also provided for all problems via the course notes, but try them before you look at the answers!