Linear models in R

Workshop notes

• Slideshow
• Workshop

Setup

This workshop is designed to work with RStudio running in Posit Cloud. Go to https://posit.cloud/ and create a new project. Monash users can log in with their Monash Google account. The workshop can also be done using R locally on your laptop (if doing this, we also recommend you create a new project to contain the files).

Running the R code below will download files and install packages used in this workshop.

# Download data
download.file(
  "https://monashdatafluency.github.io/r-linear/r-linear-files.zip",
  destfile="r-linear-files.zip")
unzip("r-linear-files.zip")

# Install some CRAN packages:
install.packages(c(
    "tidyverse", "multcomp", "emmeans", 
    "lme4", "lmerTest", "pbkrtest", "BiocManager"))

# Install some Bioconductor packages:
BiocManager::install(c("limma","edgeR","topconfects"))

Now load the file linear_models.R in the r-linear-files folder.

Files

• r-linear-files.zip - Files used in this workshop.

Key functions to remember

Built-in to R:

lm, model.matrix, coef, sigma, df.residual,
predict, confint, summary, anova, drop1, 
I, poly

splines – curve fitting:

ns, bs

multcomp and emmeans – linear hypothesis tests and multiple comparisons:

glht, mcp, confint, summary, emmeans

limma and edgeR – fitting many models to gene expression data:

DGEList, calcNormFactors, cpm,
lmFit, contrasts.fit, eBayes, plotSA, topTable

Links

• Postgraduate students at Monash can access statistical consulting, courtesy of the Data Science and AI Platform. This is a good service for beginner to intermediate statistical questions.

• The Biostatistics Consulting Platform in the Monash Faculty of Medicine may be more suitable for advanced questions about experimental design and analysis.

• Monash Data Fluency

• Monash Bioinformatics Platform

• More workshop material from Monash Bioinformatics Platform

• Course notes for PH525x. Initial chapters of this edX course cover similar material to this workshop.

• StatQuest videos on linear models. A friendly but thorough introduction to key ideas.

• Faraway (2014) “Linear models with R”

• Harrel (2015) “Regression Modeling Strategies” has detailed practical advice for creating predictive models, such as models using biomarkers. Frank Harrell’s home page.

• James, Witten, Hastie and Tibshirani (2013) “An Introduction to Statistical Learning” describes fundamental ideas and methods in machine learning.

• Dance of the CIs app for intuition about Confidence Intervals.

• The Art of Linear Algebra for intuition about matrices and vectors – sections 1-3 are relevant to this workshop.

• Testing for differential gene expression often uses linear models. The developers of limma and edgeR at WEHI have written some good introductions to this topic:

  • “RNA-seq analysis is easy as 1-2-3 with limma, Glimma and edgeR”
  • “A guide to creating design matrices for gene expression experiments” (design matrix = model matrix)
  • For samples of variable sequencing depth or quality, limma’s voom or voomWithQualityWeights can be used to account for heteroscedasticity. If using a model other than ~ 0 + group, read the note in the documentation for contrasts.fit and consider using contrastAsCoef.

• Mixed effects models are a popular next step beyond the fixed effects models covered in this workshop.

  • Mixed Models in R

Author

This course has been developed for the Monash Bioinformatics Platform and Monash Data Fluency by Paul Harrison.

This work is licensed under a Creative Commons Attribution 4.0 International License.

Source code

• GitHub repository

Solutions to challenges