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
)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
NULLuses 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 to0to show all loadings.- na.rm
Logical. Remove missing values? Default
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.
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.
See also
reliability for checking scale reliability before creating indices.
row_means for creating mean indices after identifying factors.
summary.efa for detailed output with toggleable sections.
Other scale:
pomps(),
reliability(),
row_count(),
row_means(),
row_sums()
Examples
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)
#> Exploratory Factor Analysis: 6 items, 3 components (PCA/Varimax)
#> KMO = 0.505 (Miserable), Variance explained: 61.0%
# With Oblimin rotation (requires GPArotation package)
# \donttest{
efa(survey_data,
political_orientation, environmental_concern, life_satisfaction,
trust_government, trust_media, trust_science,
rotation = "oblimin")
#> Exploratory Factor Analysis: 6 items, 3 components (PCA/Oblimin)
#> KMO = 0.505 (Miserable), Variance explained: 61.0%
# }
# Maximum Likelihood extraction
efa(survey_data,
political_orientation, environmental_concern, life_satisfaction,
trust_government, trust_media, trust_science,
extraction = "ml")
#> Exploratory Factor Analysis: 6 items, 3 components (ML/Varimax)
#> KMO = 0.505 (Miserable), Variance explained: 61.0%
# Promax rotation (oblique)
efa(survey_data,
political_orientation, environmental_concern, life_satisfaction,
trust_government, trust_media, trust_science,
rotation = "promax")
#> Exploratory Factor Analysis: 6 items, 3 components (PCA/Promax)
#> KMO = 0.505 (Miserable), Variance explained: 61.0%
# Fix number of factors
efa(survey_data,
political_orientation, environmental_concern, life_satisfaction,
trust_government, trust_media, trust_science,
n_factors = 2)
#> Exploratory Factor Analysis: 6 items, 2 components (PCA/Varimax)
#> KMO = 0.505 (Miserable), Variance explained: 44.0%
# With survey weights
efa(survey_data,
political_orientation, environmental_concern, life_satisfaction,
trust_government, trust_media, trust_science,
weights = sampling_weight)
#> Exploratory Factor Analysis: 6 items, 3 components (PCA/Varimax) [Weighted]
#> KMO = 0.505 (Miserable), Variance explained: 61.0%
# Grouped by region
survey_data %>%
group_by(region) %>%
efa(political_orientation, environmental_concern, life_satisfaction,
trust_government, trust_media, trust_science)
#> [region = 1]
#> Exploratory Factor Analysis: 6 items, 3 components (PCA/Varimax)
#> KMO = 0.475 (Unacceptable), Variance explained: 62.1%
#> [region = 2]
#> Exploratory Factor Analysis: 6 items, 3 components (PCA/Varimax)
#> KMO = 0.505 (Miserable), Variance explained: 61.3%
# --- Three-layer output ---
result <- efa(survey_data, political_orientation, environmental_concern,
life_satisfaction, trust_government, trust_media, trust_science)
result # compact overview
#> Exploratory Factor Analysis: 6 items, 3 components (PCA/Varimax)
#> KMO = 0.505 (Miserable), Variance explained: 61.0%
summary(result) # full detailed output with all sections
#>
#> Exploratory Factor Analysis (PCA, Varimax) Results
#> --------------------------------------------------
#> - Variables: political_orientation, environmental_concern, life_satisfaction, trust_government, trust_media, trust_science
#> - Extraction: Principal Component Analysis
#> - Rotation: Varimax with Kaiser Normalization
#> - N of Factors: 3
#>
#> KMO and Bartlett's Test
#> ----------------------------------------
#> Kaiser-Meyer-Olkin Measure: 0.505
#> Bartlett's Chi-Square: 932.068
#> df: 15
#> Sig.: 0.000
#>
#> Communalities
#> ----------------------------------------
#> variable initial extraction
#> political_orientation 1 0.786
#> environmental_concern 1 0.783
#> life_satisfaction 1 0.668
#> trust_government 1 0.347
#> trust_media 1 0.475
#> trust_science 1 0.598
#> Extraction Method: Principal Component Analysis.
#>
#> Total Variance Explained
#> ----------------------------------------
#> PC1 Eigenvalue: 1.600 Variance: 26.666% Cumulative: 26.666%
#> PC2 Eigenvalue: 1.041 Variance: 17.358% Cumulative: 44.024%
#> PC3 Eigenvalue: 1.017 Variance: 16.955% Cumulative: 60.979%
#> PC4 Eigenvalue: 0.980 Variance: 16.334% Cumulative: 77.313%
#> PC5 Eigenvalue: 0.949 Variance: 15.814% Cumulative: 93.127%
#> PC6 Eigenvalue: 0.412 Variance: 6.873% Cumulative: 100.000%
#>
#> Rotation Sums of Squared Loadings
#> ----------------------------------------
#> PC1 SS Loading: 1.598 Variance: 26.634% Cumulative: 26.634%
#> PC2 SS Loading: 1.039 Variance: 17.325% Cumulative: 43.959%
#> PC3 SS Loading: 1.021 Variance: 17.020% Cumulative: 60.979%
#>
#> Component Matrix (unrotated)
#> ----------------------------------------
#> PC1 PC2 PC3
#> political_orientation 0.885
#> environmental_concern -0.885
#> trust_science -0.672
#> trust_government -0.547
#> trust_media -0.524 -0.448
#> life_satisfaction -0.809
#> Extraction Method: Principal Component Analysis.
#>
#> Rotated Component Matrix
#> ----------------------------------------
#> PC1 PC2 PC3
#> political_orientation 0.887
#> environmental_concern -0.884
#> trust_science -0.762
#> trust_government -0.566
#> life_satisfaction -0.789
#> trust_media -0.620
#> Extraction Method: Principal Component Analysis.
#> Rotation Method: Varimax with Kaiser Normalization.
summary(result, communalities = FALSE) # hide communalities table
#>
#> Exploratory Factor Analysis (PCA, Varimax) Results
#> --------------------------------------------------
#> - Variables: political_orientation, environmental_concern, life_satisfaction, trust_government, trust_media, trust_science
#> - Extraction: Principal Component Analysis
#> - Rotation: Varimax with Kaiser Normalization
#> - N of Factors: 3
#>
#> KMO and Bartlett's Test
#> ----------------------------------------
#> Kaiser-Meyer-Olkin Measure: 0.505
#> Bartlett's Chi-Square: 932.068
#> df: 15
#> Sig.: 0.000
#>
#> Total Variance Explained
#> ----------------------------------------
#> PC1 Eigenvalue: 1.600 Variance: 26.666% Cumulative: 26.666%
#> PC2 Eigenvalue: 1.041 Variance: 17.358% Cumulative: 44.024%
#> PC3 Eigenvalue: 1.017 Variance: 16.955% Cumulative: 60.979%
#> PC4 Eigenvalue: 0.980 Variance: 16.334% Cumulative: 77.313%
#> PC5 Eigenvalue: 0.949 Variance: 15.814% Cumulative: 93.127%
#> PC6 Eigenvalue: 0.412 Variance: 6.873% Cumulative: 100.000%
#>
#> Rotation Sums of Squared Loadings
#> ----------------------------------------
#> PC1 SS Loading: 1.598 Variance: 26.634% Cumulative: 26.634%
#> PC2 SS Loading: 1.039 Variance: 17.325% Cumulative: 43.959%
#> PC3 SS Loading: 1.021 Variance: 17.020% Cumulative: 60.979%
#>
#> Component Matrix (unrotated)
#> ----------------------------------------
#> PC1 PC2 PC3
#> political_orientation 0.885
#> environmental_concern -0.885
#> trust_science -0.672
#> trust_government -0.547
#> trust_media -0.524 -0.448
#> life_satisfaction -0.809
#> Extraction Method: Principal Component Analysis.
#>
#> Rotated Component Matrix
#> ----------------------------------------
#> PC1 PC2 PC3
#> political_orientation 0.887
#> environmental_concern -0.884
#> trust_science -0.762
#> trust_government -0.566
#> life_satisfaction -0.789
#> trust_media -0.620
#> Extraction Method: Principal Component Analysis.
#> Rotation Method: Varimax with Kaiser Normalization.