Multivariate Analysis with R

Worked examples of the standard multivariate methods in R, applied to survey data: PCA, factor analysis, clustering, MANOVA, discriminant analysis, and ordination.

Each method has a notebook that reads as a report. The shared cleaning, diagnostic, and plotting code lives in R/ so the notebooks carry analysis rather than boilerplate.

Methods

Notebook	Method	What it answers
notebook/PCA.Rmd	Principal components	Which dimensions carry the variance
notebook/Factor Analysis.Rmd	Factor analysis	Which latent factors explain the correlations
notebook/Clustering.Rmd	k means and hierarchical	Which respondents group together
notebook/Manova.Rmd	MANOVA and MANCOVA	Whether group means differ across several outcomes
notebook/Discriminant.Rmd, Discriminant2.Rmd	LDA and QDA	Which variables separate known groups
notebook/Ordination Analysis.Rmd	CA, CCA, NMDS	How rows and columns relate in low dimensions

clustering/Clustering.Rmd is a longer version of the clustering analysis, and notebook/Clustering_project/ holds a written up variant with its data and rendered pdf.

Layout

R/setup.R          package groups, installing and loading, plus load_modules()
R/survey.R         reading exports, dropping descriptors, filtering, mode imputation, typing
R/multiselect.R    expanding select all that apply answers into indicator columns
R/diagnostics.R    multivariate normality by block, outliers, correlation, factorability
R/pca.R            fitting, variance explained, retention rules, loadings, plots
R/clustering.R     distances, choosing k, k means, hierarchical, silhouette, profiles
scripts/run-pca.R  the PCA pipeline end to end from the command line
tests/             base R checks that need no data
notebook/          the analyses, one per method
legacy/            the original PCA script, kept for reference

Using it

source("R/setup.R")
load_modules()
load_packages(install = TRUE)

In a notebook that replaces the whole library block. From the command line:

Rscript scripts/run-pca.R "Travel Study 2.7.23.csv" output

Tables and charts land in output/. The survey csv is not in this repository.

Tests

Rscript tests/test-functions.R

20 checks over mode imputation, survey filtering, column dropping, type coercion, PCA variance accounting, and block splitting. Base R only, so they run without the modelling packages installed.

What changed

The analyses were unchanged in substance. The repetition around them was the problem.

Before	After
The same eleven line library block in 10 files	load_packages() with named groups
calc_mode defined 8 separate times	once in R/survey.R
3 near identical blocks expanding multi select answers	expand_all_multiselect() over a mapping
7 hand written mvn() calls over column ranges	normality_by_block()
Cleaning steps repeated per notebook	composable functions in R/survey.R
670 KB of .RData and .Rhistory committed	removed and ignored

The old src/PCA.R also carried a stray df = re assignment and read an input.xml that the rest of the script never used, both leftovers from an earlier draft. scripts/run-pca.R replaces it, and the original is kept at legacy/pca-original.R.

Status

Verified on R 4.6.1: every module parses, and the checks above pass.

Not reproduced end to end. The survey csv is not in the repository, so the fitting and plotting paths have not been run against real data. Treat the first run as a replication check.

The notebooks still contain their original inline code. They are the record of the analyses as written, so they were left intact rather than rewritten, and the modules are available to them whenever you want to trim one down.

License

See the repository. Original analyses 2023.