Parallel Analysis for Factor Retention

Parallel analysis decides how many components or factors to retain by keeping only those whose observed eigenvalues exceed the corresponding eigenvalues from random data of the same size.

평행분석은 같은 크기의 무작위 자료에서 얻은 고유값보다 관측 고유값이 큰 성분이나 요인만 남겨 추출할 개수를 정하는 방법입니다.

How many factors should I extract from my 20-item questionnaire before running factor analysis?

20문항 설문으로 요인분석을 하기 전에 요인을 몇 개 뽑아야 하는지 어떻게 정하나요?

Parallel analysis compares the eigenvalues of the observed correlation matrix with a chosen percentile, usually the 95th, of eigenvalues obtained from many random normal data sets with the same number of cases and items. Components or factors are retained while their observed eigenvalue exceeds the random benchmark, which avoids the over-extraction typical of the eigenvalue-greater-than-one rule.

When to use Parallel Analysis for Factor Retention

• You are about to run exploratory factor analysis or PCA and need to choose the number of dimensions.
• You want a retention criterion that is less prone to over-extraction than the Kaiser rule.
• Items are continuous or approximately interval-scaled.

When to use something else

• The number of factors is fixed by theory and needs confirmation; use confirmatory factor analysis instead.
• Items are binary or few-category ordinal and strongly skewed; use parallel analysis on polychoric correlations instead.

Assumptions and requirements

• Items are measured on an approximately interval scale.
• The correlation matrix is not singular.
• An adequate sample size relative to the number of items.

What the analysis reports

• Observed PCA and common-factor eigenvalues
• Mean and 95th-percentile eigenvalues from random data
• Number of components and factors to retain
• Comparison with the Kaiser criterion

How to report it

Horn's parallel analysis ([B] random data sets, 95th percentile criterion; N = [n], [p] items) suggested retaining [k] factors.

Related methods

• Exploratory Factor Analysis (EFA)
• Principal Component Analysis (PCA)
• Confirmatory Factor Analysis (CFA)

Run Parallel Analysis for Factor Retention on Quorant