# kfa: K-Fold Cross-Validation For Factor Analysis

kfa provides utilities for examining the dimensionality of a set of variables to foster scale development. Harnessing a k-fold cross-validation approach, kfa helps researchers compare possible factor structures and identify which structures are plausible and replicable across samples.

## Installation

# From CRAN
install.packages("kfa")

# Development version
install.packages("remotes")
remotes::install_github("knickodem/kfa")

library(kfa)

## Workflow

The two primary functions are kfa() and kfa_report(). When the set of potential variables and (optionally) the maximum number of factors, m, are supplied to kfa(), the function:

• (if requested) conducts a power analysis to determine the number of folds, k, on which to split the data into training and testing samples
• creates k folds (i.e. the training and testing samples).

Then for each fold:

• calculates sample statistics (e.g., correlation matrix, thresholds [if necessary]) from training sample.
• runs 2:m factor exploratory factor analysis (EFA) models using the sample statistics, applies rotation (if specified), and extracts the factor structure for a confirmatory factor analysis (CFA). The structure for a 1-factor CFA is also defined.
• runs the 1:m factor CFA models on the testing sample.

The factor analyses are run using the lavaan package with many of the lavaan estimation and missing data options available for use in kfa(). kfa() returns a list of lists with k outer elements for each fold and m inner elements for each replicable factor model, each containing a lavaan object. To expedite running k x m x 2 (EFA and CFA) models, the function utilizes the parallel and foreach packages for parallel processing.

library(kfa)
sim.mod <- "f1 =~ .7*x1 + .8*x2 + .3*x3 + .7*x4 + .6*x5 + .8*x6 + .4*x7
f2 =~ .8*x8 + .7*x9 + .6*x10 + .5*x11 + .5*x12 + .7*x13 + .6*x14
f3 =~ .6*x15 + .5*x16 + .9*x17 + .4*x18 + .7*x19 + .5*x20
f1 ~~ .2*f2
f2 ~~ .2*f3
f1 ~~ .2*f3
x9 ~~ .2*x10"
set.seed(1161)
sim.data <- simstandard::sim_standardized(sim.mod,
n = 900,
latent = FALSE,
errors = FALSE)[c(2:9,1,10:20)]

# include a custom 2-factor model
custom2f <- paste0("f1 =~ ", paste(colnames(sim.data)[1:10], collapse = " + "),
"\nf2 =~ ",paste(colnames(sim.data)[11:20], collapse = " + "))

mods <- kfa(data = sim.data,
k = NULL,    # NULL prompts power analysis to determine number of folds
custom.cfas = custom2f  # can be a single object or named list
)

kfa_report() then aggregates the CFA model fit, parameter estimates, and model-based reliability across folds for each factor structure extracted in kfa(). The results are then organized and exported via rmarkdown, such as the example report run below.

# Run report
kfa_report(models = mods,
file.name = "example_sim_kfa_report",
report.title = "K-fold Factor Analysis - Example Sim",
report.format = "html_document")

## Under Development and Consideration

• Clustered Data - The package does not currently account for clustered data. Future versions will utilize the cluster argument from lavaan to estimate cluster robust standard errors when calculating the correlation matrix for the factor analyses. We are also considering how to account for nesting structures in the creation of the folds, which are currently created assuming a simple random sample. If so, we will also incorporate cluster adjustments for the power analysis determining the value of k.