Exploratory factor analysis in R is used to identify latent constructs behind survey items, psychological scales, and multi-item research instruments. When several observed variables are correlated, EFA helps determine whether they can be grouped into a smaller number of underlying factors.

Many student projects lose marks because factor analysis is run mechanically without adequacy checks, justified retention decisions, or correct interpretation of loadings. Reviewers expect methodological justification, not only software output. This guide presents the full workflow, including preparation, assumption testing, extraction, rotation, diagnostics, and thesis-ready interpretation examples.

By the end, you will know how to run exploratory factor analysis in R and how to report it correctly.

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What Exploratory Factor Analysis Does

Exploratory factor analysis models shared variance across observed variables and estimates latent factors that explain the correlation structure. Instead of analyzing each item separately, EFA groups items into interpretable dimensions.

It helps answer:

• how many latent constructs exist
• which items belong to each construct
• how strongly each item loads
• how much variance is explained

Common applications include scale development, construct validation, and questionnaire reduction.

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Sample Size and Data Requirements

Before running exploratory factor analysis in R, confirm that your dataset is adequate.

Recommended practice includes at least five to ten observations per item, with a preferred total sample above 200 where possible. Variables should be numeric and measured on interval or Likert-type scales. Inter-item correlations should be present but not extreme.

Small samples often produce unstable factor structures and poor replication.

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Required R Packages

Install and load the main packages used for EFA.

install.packages("psych")
install.packages("GPArotation")
install.packages("nFactors")

library(psych)
library(GPArotation)
library(nFactors)

The psych package provides the primary exploratory factor analysis functions.

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Data Preparation Steps

Prepare your dataset before extraction. First remove or handle missing values. Next ensure all items are numeric. Then reverse code negatively worded items so that scale direction is consistent.

items <- na.omit(items)
items[] <- lapply(items, as.numeric)

# example reverse coding
items$Q3 <- 6 - items$Q3

Failure to reverse code produces distorted factor loadings.

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Choosing the Correlation Matrix

For Likert-type ordinal data, polychoric correlations are often more appropriate. For continuous data, Pearson correlations are acceptable.

poly <- polychoric(items)
cor_mat <- poly$rho

or

cor_mat <- cor(items)

The correlation matrix is the foundation of exploratory factor analysis in R.

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Factorability Tests

Adequacy testing should always be reported.

KMO Measure

KMO(cor_mat)

Values above 0.70 are generally acceptable.

Bartlett Test

cortest.bartlett(cor_mat, n = nrow(items))

A significant result indicates that factor analysis is appropriate.

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Determining the Number of Factors

Factor retention must be justified using multiple criteria.

Parallel Analysis

fa.parallel(items, fa="fa")

Parallel analysis is one of the most defensible methods.

Eigenvalues

eigen(cor_mat)$values

Values above one are sometimes retained, although this rule alone is weak.

Scree Plot

Use elbow location as supporting evidence rather than the sole rule.

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Extraction Methods in Exploratory Factor Analysis in R

Common extraction methods include principal axis factoring, maximum likelihood, and minimum residual. Principal axis and minimum residual are robust defaults.

efa <- fa(items, nfactors=3, fm="pa", rotate="oblimin")

Extraction choice should be stated in your methodology.

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Rotation Methods and When to Use Them

Rotation improves interpretability.

Oblique rotations such as oblimin or promax allow factors to correlate and are commonly used in social science research. Orthogonal rotation such as varimax forces independence and is used when theory requires uncorrelated factors.

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Running the EFA Model in R

Run the model with chosen factor count, extraction, and rotation.

efa_model <- fa(items,
                nfactors=3,
                fm="pa",
                rotate="oblimin")

print(efa_model, cutoff=.30)

The cutoff hides trivial loadings for readability.

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Interpreting Factor Loadings

Factor loadings show the strength of association between items and factors. Strong primary loadings with low cross-loadings indicate clean structure. Items with weak loadings or heavy cross-loadings are candidates for removal.

Thresholds of 0.40 or higher are commonly used in student research.

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Communalities and Variance Explained

Communalities indicate how much variance in each item is explained by the factor model.

efa_model$communality

Values above 0.40 are typically acceptable. Also report total and cumulative variance explained by retained factors.

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Naming the Factors

Factor naming is theory driven. Review the highest loading items per factor, examine their wording, then assign a construct label that reflects shared meaning. Do not name factors based on statistics alone.

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Reliability After Factor Extraction

Internal consistency should be tested for each factor.

alpha(items[,c("Q1","Q2","Q3")])

Report reliability coefficients in your results section.

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Sample Interpretation of Exploratory Factor Analysis in R

An exploratory factor analysis in R was conducted using principal axis factoring with oblimin rotation. The KMO value was 0.86 and Bartlett’s test was significant, indicating suitability. Parallel analysis supported a three-factor solution explaining 64 percent of variance. Items loaded strongly on their respective factors with minimal cross-loading, and reliability values exceeded 0.78. The factors were interpreted as Motivation, Confidence, and Engagement based on item content.

Common Examiner Red Flags to avoid

• No KMO or Bartlett reported
• Factor count chosen without parallel analysis
• Using PCA and calling it EFA
• Keeping weak loadings
• Ignoring cross-loadings
• No reliability analysis
• No theoretical justification for factor names

Confirmatory Factor Analysis vs Exploratory Factor Analysis

Researchers use exploratory factor analysis and confirmatory factor analysis for related purposes; however, each method answers a different type of measurement question. Therefore, you should choose the method based on your research stage and theoretical clarity.

Exploratory factor analysis in R helps you discover the underlying factor structure when you do not yet know how items group together. In this approach, you let the data reveal the factor pattern. You examine how variables cluster, how many latent factors emerge, and which items load most strongly on each factor.

In contrast, confirmatory factor analysis tests a structure that you already defined in advance. You begin with a theoretical model, assign items to specific factors, and then evaluate how well the data fits that model. As a result, CFA supports theory testing, while EFA supports structure discovery.

Because of this distinction, researchers typically run exploratory factor analysis first and then apply confirmatory factor analysis later for validation.

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Key Differences Between EFA and CFA

First, exploratory factor analysis allows every item to load on multiple factors during estimation. You then review the loading matrix and refine the structure based on strength and clarity. Consequently, cross-loadings often appear in early EFA solutions and guide item removal decisions.

By comparison, confirmatory factor analysis requires you to specify item–factor relationships before estimation. You assign each item to a target factor and restrict cross-loadings unless theory strongly justifies them. Then you evaluate how well the proposed structure fits the observed covariance matrix.

Moreover, each method relies on different evaluation criteria. EFA focuses on factor loadings, communalities, and variance explained. On the other hand, CFA relies on model fit indices such as CFI, TLI, RMSEA, and SRMR to judge adequacy.

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When to Use Exploratory Factor Analysis in R

You should choose exploratory factor analysis in R when you develop a new scale or when theory does not clearly define the factor structure. For example, you may work with a new questionnaire, mixed constructs, or an adapted instrument. In these cases, EFA gives you empirical guidance about item grouping.

Furthermore, EFA works well when you want to reduce a large pool of survey items into a smaller, interpretable set of dimensions. Instead of forcing a model too early, you let the correlation structure guide your decisions.

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When Confirmatory Factor Analysis Fits Better

You should use confirmatory factor analysis when strong theory or prior validation already defines the factor structure. For instance, you may replicate a published scale, test measurement invariance, or verify a known construct model. Under these conditions, CFA gives you a direct model test.

In addition, CFA helps you compare competing theoretical models and select the one that fits best. You can therefore support stronger construct validity claims.

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Practical Workflow: Use EFA First, Then CFA

In practice, many strong studies follow a two-step workflow. First, researchers run exploratory factor analysis in R to identify the factor structure and remove weak items. Next, they collect a new sample and run confirmatory factor analysis to test that refined structure.

This sequence improves measurement quality and increases methodological credibility. As a result, supervisors and reviewers often view EFA-then-CFA designs more favorably than single-stage analyses.