Introduction to OptimalFactor

Overview

OptimalFactor is a comprehensive R package for optimal factor model refinement in both Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA) using machine-learning inspired boosting algorithms.

Installation

You can install the latest version of OptimalFactor from GitHub:

if (!require("devtools")) {
  install.packages("devtools")
}
devtools::install_github("jventural/OptimalFactor")

Main Features

EFA-Boosting Algorithm

The efa_boosting() function implements an advanced iterative optimization algorithm for EFA:

Greedy and global search strategies for optimal item selection
Adaptive composite fit indices (RMSEA, SRMR, CFI) with weights based on df x N
Automatic Heywood case and near-Heywood detection
Cross-loading identification and removal
Minimum items per factor enforcement
Interfactor correlation verification
Optional AI-assisted conceptual analysis via GPT models

CFA Optimization

The cfa_boosting() function provides CFA optimization:

Modification indices-based model improvement
Automatic covariance addition
Fit index monitoring

Quick Start

Basic EFA-Boosting

library(OptimalFactor)

# Run EFA-Boosting
result <- efa_boosting(
  data = your_data,
  name_items = "item",
  n_factors = 3,
  verbose = TRUE
)

# View results
print(result$final_structure)
print(result$fit_indices)

Theoretical Background

The EFA-Boosting algorithm uses adaptive fit indices based on the research by Kenny and McCoach (2003) and Shi, Lee, & Maydeu-Olivares (2019), which demonstrates that traditional cutoff values for fit indices depend on model complexity (degrees of freedom) and sample size.

The adaptive weights are calculated as:

RMSEA weight: Higher for larger models (more df)
SRMR weight: Stable across model sizes
CFI weight: Higher for smaller models (fewer df)

This adaptive approach ensures appropriate model evaluation across different scales and sample sizes.

References

Kenny, D. A., & McCoach, D. B. (2003). Effect of the number of variables on measures of fit in structural equation modeling. Structural Equation Modeling, 10(3), 333-351.
Shi, D., Lee, T., & Maydeu-Olivares, A. (2019). Understanding the model size effect on SEM fit indices. Educational and Psychological Measurement, 79(2), 310-334.