The BayesianEFA package provides a straightforward way to estimate Bayesian Exploratory Factor Analysis (EFA) models via Stan.
While the package supports both rstan and cmdstanr, the use of cmdstanr is highly recommended as it is the only backend that ensures compatibility with the latest version of Stan and typically offers faster estimation times. Please install cmdstanr by following the official guide.
Installation in Windows and Linux
You can install the development version of BayesianEFA from GitHub with:
# install.packages("devtools")
devtools::install_github("RicardoReySaez/BayesianEFA", force = TRUE)Please be a little patient during installation! It will take several minutes to compile the underlying Stan models. Grab a coffee and don’t worry if it seems to be taking a while, it’s completely normal.
Installation in macOS
Since BayesianEFA includes custom C++ functions, macOS users must configure the R compilation toolchain. Following the recommendations from the latent package, we suggest using macrtools by James Balamuta to automate this setup:
# 1. Install macrtools
# install.packages("remotes")
remotes::install_github("coatless-mac/macrtools")
# 2. Setup the toolchain and OpenMP support
macrtools::macos_rtools_install()
macrtools::openmp_install()
# 3. Install BayesianEFA
devtools::install_github("RicardoReySaez/BayesianEFA", force = TRUE)Important: GitHub Actions routinely test the package against the latest macOS environments, so keeping your system updated is the best way to avoid compilation errors. If errors persist, we highly recommend pasting the compilation output into a Large Language Model (e.g., ChatGPT, Gemini, Claude) for quick troubleshooting.
Quick Start
Here is a basic example showing how to fit a Bayesian EFA model:
library(BayesianEFA)
# Fit a 3-factor Bayesian EFA model using the Holzinger & Swineford dataset
befa_fit <- befa(data = HS_data, n_factors = 3, seed = 17)
# Print a comprehensive summary of the model (inspired in psych package output)
summary(befa_fit, cutoff = 0.3, signif_stars = TRUE)
# Table 1. Factor Loadings (Pattern Matrix)
# ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
# Variable F1 F2 F3 h2 u2 Rhat EssBulk EssTail
# ———————————————————————————————————————————————————————————————————
# Item_1 0.59* 0.31* 0.47 0.53 1.00 3458 2849
# Item_2 0.46* 0.23 0.77 1.00 4053 2741
# Item_3 0.65* 0.44 0.56 1.00 4146 2274
# Item_4 0.83* 0.71 0.29 1.00 4156 2607
# Item_5 0.86* 0.75 0.25 1.00 4179 2983
# Item_6 0.81* 0.68 0.32 1.00 4291 2817
# Item_7 0.68* 0.48 0.52 1.00 3343 2081
# Item_8 0.69* 0.52 0.48 1.00 3614 2593
# Item_9 0.40* 0.49* 0.43 0.57 1.00 3014 2757
# ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
# Note: varimax rotation applied. Diagnostics show worst-case values
# across factors (max Rhat, min ESS). The 3 latent factors accounted
# for 52.2% of total variance. (*) 95% Credible Interval excludes 0.
# Loadings with absolute values < 0.30 are hidden.
#
# Table 2. Bayesian Fit Measures
# ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
# Index Estimate SD CI_Low CI_High
# —————————————————————————————————————————————————
# Chi2 47.75 7.24 35.81 63.71
# Chi2_ppp 0.11
# Chi2_Null 918.85 0.00 918.85 918.85
# BRMSEA 0.06 0.02 0.00 0.09
# BGamma 0.99 0.01 0.98 1.00
# Adj_BGamma 0.97 0.02 0.93 1.00
# BMc 0.98 0.01 0.96 1.00
# SRMR 0.05 0.01 0.03 0.06
# BCFI 0.99 0.01 0.97 1.00
# BTLI 0.99 0.02 0.93 1.00
# ELPD -3416.93 42.49 -3500.21 -3333.64
# LOOIC 6833.85 84.98 6667.29 7000.42
# p_loo 25.58 1.82 22.01 29.14
# ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
# Note: Intervals are 95% Credible Intervals. PPP:
# Posterior Predictive p-value (Ideal > .05).
# p_loo/LOOIC derived from PSIS-LOO.
#
# Table 3. Factor Reliability (Coefficient Omega)
# ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
# Factor Estimate SD CI_Low CI_High
# —————————————————————————————————————————
# F1 0.60 0.04 0.52 0.67
# F2 0.73 0.02 0.69 0.76
# F3 0.55 0.04 0.45 0.62
# ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
# Full Scale Omega Total: 0.84 [0.82,
# 0.86]. Omega coefficients use the full
# posterior distribution. For a complete guide on how to perform a Bayesian EFA from scratch, please visit the Getting Started tutorial or explore the comprehensive package website!