FactorUtils

Utilities for Factor Analysis in Julia.

This package is essentially a high-level wrapper around MultivariateStats.jl and FactorRotations.jl.

It centres on methods fa and pca that take DataFrames, and return FactorResults objects which store not only the FactorAnalysis output from MultivariateStats but also the variable names.

These objects then produce output as prettier DimArrays from DimensionalData.jl and can be called with pretty() to provide informative output about the model. biplot() and indplot() methods are also provided for Makie.

NB while MultivariateStats uses variable * observation matrices, this package uses observation * variable matrices.

Methods exported

See the documentation for arguments.

• fa: Factor Analysis on a DataFrame
• efa: EFA on the output of fa
• pca: Principal Component Analysis on a DataFrame

All methods from MultivariateStats (e.g. loadings, mean, eigvals etc.) work on the FactorResults outputs from those functions.

• prep_data: Checks missing-ness and drops non-numeric or sum-to-0 columns

• normalise: A wrapper around StatsBase.ZScoreTransform

• pretty: Highlgihted pretty output for a DimArray

• cos2_ind: get cos2 (contribution) score by individual

• cos2_var: get cos2 (contribution) score by variable (= squared loadings)

• unique_variance: get unique variance not captured for each variable (= 1 - sum of squared loadings).

• variance_explained: get unique variance not captured for each variable (= 1 - sum of squared loadings).

• biplot: Quick variable biplot for FactorResults object. Loaded with Makie if a Makie backend is imported.

• indplot: Quick individuals plot for FactorResults object. Loaded with Makie if a Makie backend is imported.

• biplotarrows: Internal plot method for variable biplot. Requires importing a Makie backend

• indscatter: quick individual plot on factor axes. Requires importing a Makie backend

• efa_lavaan: uses R to take the output from the lavaan implementation of EFA. Do using RCall first to make this method available.

Example

using FactorUtils
using RDatasets

bfi_all = dataset("psych", "bfi")[:,2:26]
# Handle missing data properly, this is just an e.g
bfi = dropmissing(bfi_all)

# PCA
pca1 = pca(bfi, 5)

# Show loadings and variance explained
pretty(pca1)

# Get some statistics
eigvals(pca1)
loadings(pca1) |> pretty
cos2_ind(pca1)
variance_explained(pca1)

# Predict calls on data used for prediction
predict(pca1)
# or can be passed new data as observations * vars, scaling is applied
predict(pca1, bfi[1:10,:])
predict(pca1, bfi[1:10,:]; apply_scaling=false)

# show biplot
using GLMakie
biplot(pca1; max_labels=20)
indplot(pca1)

# show individuals plot and customise
fig, ax = indplot(pca1)
ax.xlabel = "My own label..."

# FA
fa1 = fa(bfi, 5)
# rotate
# preferred to FactorUtils.rotate! since it uses many repeats by default
efa1 = efa(fa1, Geomin()) 
pretty(efa1)
loadings(efa1)
predict(efa1)

# Lavaan efa - note the warning
using RCall
efa2 = efa_lavaan(bfi, 5, "geomin")
pretty(loadings(efa2))

TODO

Add proper tests for Makie plots.

Allow biplot!() and indplot!() methods to work.