efa: Explore the Structure Behind Your Survey Items

Description

efa() performs Exploratory Factor Analysis (EFA) to discover underlying patterns in your survey items. Supports both Principal Component Analysis (PCA) and Maximum Likelihood (ML) extraction. This is the R equivalent of SPSS's FACTOR procedure.

For example, if you have 6 items measuring different attitudes, EFA can reveal whether they group into 2-3 underlying dimensions (factors or components).

Usage

efa(
  data,
  ...,
  n_factors = NULL,
  rotation = "varimax",
  extraction = "pca",
  weights = NULL,
  use = "pairwise",
  sort = TRUE,
  blank = 0.4,
  na.rm = TRUE
)

Value

An efa result object containing:

loadings: Component loading matrix (rotated if rotation applied)
unrotated_loadings: Unrotated component matrix
eigenvalues: All eigenvalues from the correlation matrix
variance_explained: Tibble with Total, % of Variance, Cumulative %
rotation_variance: Tibble with rotation sums of squared loadings
communalities: Extraction communalities for each variable
kmo: List with overall KMO and per-item MSA values
bartlett: List with chi_sq, df, and p_value
rotation: Rotation method used
extraction: Extraction method used
n_factors: Number of components extracted
correlation_matrix: Correlation matrix used for analysis
initial_communalities: Initial communalities (1.0 for PCA, SMC for ML)
goodness_of_fit: Goodness-of-fit test (ML only): chi_sq, df, p_value. NULL for PCA.
uniquenesses: Unique variances per variable (ML only, NULL for PCA)
pattern_matrix: Pattern matrix (oblimin/promax only, NULL otherwise)
structure_matrix: Structure matrix (oblimin/promax only, NULL otherwise)
factor_correlations: Factor correlation matrix (oblimin/promax only, NULL otherwise)
variables: Character vector of variable names
weights: Weights variable name or NULL
n: Sample size
col_prefix: Column name prefix: "PC" for PCA, "Factor" for ML
sort: Whether loadings are sorted
blank: Suppression threshold

Use summary() for the full SPSS-style output with toggleable sections.

Arguments

data: Your survey data (a data frame or tibble)
...: The items to analyze. Use bare column names separated by commas, or tidyselect helpers like starts_with("trust").
n_factors: Number of components to extract. Default NULL uses the Kaiser criterion (eigenvalue > 1).
rotation: Rotation method: "varimax" (default, orthogonal), "oblimin" (oblique, allows correlated factors), "promax" (oblique, power-based), or "none".
extraction: Extraction method: "pca" (default, Principal Component Analysis) or "ml" (Maximum Likelihood, enables goodness-of-fit testing, assumes multivariate normality).
weights: Optional survey weights for population-representative results.
use: How to handle missing data for correlation computation: "pairwise" (default, matches SPSS) or "complete" (listwise).
sort: Logical. Sort loadings by size within each component? Default TRUE.
blank: Numeric. Suppress (hide) loadings with absolute value below this threshold in the print output. Default 0.40 (matches SPSS BLANK(.40)). Set to 0 to show all loadings.
na.rm: Logical. Remove missing values? Default TRUE.

Details

Understanding the Results

KMO (Kaiser-Meyer-Olkin) measures sampling adequacy:

KMO > 0.90: Marvelous
KMO 0.80 - 0.90: Meritorious
KMO 0.70 - 0.80: Middling
KMO 0.60 - 0.70: Mediocre
KMO 0.50 - 0.60: Miserable
KMO < 0.50: Unacceptable - don't use factor analysis

Bartlett's Test of Sphericity tests whether correlations are significantly different from zero. A significant result (p < .05) means the correlation matrix is suitable for factor analysis.

Eigenvalues indicate how much variance each component explains. The Kaiser criterion retains components with eigenvalue > 1.

Factor Loadings show how strongly each item relates to each component:

|loading| > 0.70: Strong association
|loading| 0.40 - 0.70: Moderate association
|loading| < 0.40: Weak (suppressed by default)

Communalities show how much of each item's variance is explained by the extracted components. Low communalities (< 0.40) suggest the item doesn't fit well with the others.

Choosing an Extraction Method

PCA (default): Extracts components explaining maximum total variance. Simple and robust. Does not assume normality.
ML: Extracts factors explaining shared variance only. Assumes multivariate normality. Provides a goodness-of-fit test to evaluate model fit. A non-significant chi-square (p > .05) suggests adequate fit.

Choosing a Rotation

Varimax (default): Assumes factors are uncorrelated. Produces simpler, easier-to-interpret results.
Oblimin: Allows factors to be correlated. More realistic for social science data. Produces both a Pattern Matrix (unique contributions) and Structure Matrix (total correlations).
Promax: Oblique rotation based on a power transformation of Varimax results. Like Oblimin, produces Pattern and Structure matrices. Common alternative to Oblimin in SPSS.
None: No rotation. Rarely useful for interpretation.

Examples

Run this code

library(dplyr)
data(survey_data)

# Basic EFA with Varimax rotation
efa(survey_data,
    political_orientation, environmental_concern, life_satisfaction,
    trust_government, trust_media, trust_science)

# With Oblimin rotation (requires GPArotation package)
# \donttest{
if (requireNamespace("GPArotation", quietly = TRUE)) {
  efa(survey_data,
      political_orientation, environmental_concern, life_satisfaction,
      trust_government, trust_media, trust_science,
      rotation = "oblimin")
}
# }

# Maximum Likelihood extraction
efa(survey_data,
    political_orientation, environmental_concern, life_satisfaction,
    trust_government, trust_media, trust_science,
    extraction = "ml")

# Promax rotation (oblique)
efa(survey_data,
    political_orientation, environmental_concern, life_satisfaction,
    trust_government, trust_media, trust_science,
    rotation = "promax")

# Fix number of factors
efa(survey_data,
    political_orientation, environmental_concern, life_satisfaction,
    trust_government, trust_media, trust_science,
    n_factors = 2)

# With survey weights
efa(survey_data,
    political_orientation, environmental_concern, life_satisfaction,
    trust_government, trust_media, trust_science,
    weights = sampling_weight)

# Grouped by region
survey_data %>%
  group_by(region) %>%
  efa(political_orientation, environmental_concern, life_satisfaction,
      trust_government, trust_media, trust_science)

# --- Three-layer output ---
result <- efa(survey_data, political_orientation, environmental_concern,
              life_satisfaction, trust_government, trust_media, trust_science)
result              # compact overview
summary(result)     # full detailed output with all sections
summary(result, communalities = FALSE)  # hide communalities table

Run the code above in your browser using DataLab