# Retention methods in exploratory factor analysis (EFA)

Retention methods in exploratory factor analysis (EFA) involve determining how many factors to retain from the initial factor extraction. The goal is to identify a meaningful and interpretable number of factors that adequately represent the underlying structure of the observed variables. Several common retention methods are used for this purpose:

1. Kaiser’s Criterion:
• Proposed by Kaiser, this method suggests retaining factors with eigenvalues greater than 1. The eigenvalue represents the amount of variance explained by each factor. Factors with eigenvalues less than 1 are considered to contribute less variance than a single variable, so they are typically excluded.
2. Scree Plot Inspection:
• The scree plot is a graphical representation of the eigenvalues in descending order. The point where the curve levels off (referred to as the “elbow” of the scree plot) indicates the number of factors to retain. Factors before the elbow are considered meaningful, while those after it are often considered noise.
• This method is somewhat subjective, and researchers may visually inspect the scree plot to determine the appropriate number of factors.
3. Parallel Analysis:
• Parallel analysis is a statistical technique that compares the eigenvalues obtained from the actual data with those obtained from randomly generated data (typically through Monte Carlo simulations) with no underlying factors.
• The number of factors to retain is determined by comparing the actual eigenvalues with the average eigenvalues from the random data. Factors with eigenvalues surpassing the corresponding average eigenvalues are retained.
4. Minimum Average Partial (MAP) Test:
• The MAP test involves examining the average partial correlation coefficients for different factor solutions. The solution with the lowest average partial correlation is considered the most interpretable.
• Researchers can examine the average partial correlations for various factor solutions and choose the solution that minimizes these values.
5. Velicer’s Minimum Average Partial (MAP) Test:
• Similar to the MAP test, Velicer’s MAP test calculates the average squared partial correlations across different factor solutions. The number of factors corresponding to the minimum average squared partial correlation is retained.

It’s important to note that these retention methods provide guidance, but they are not definitive rules. The choice of the number of factors often involves a combination of statistical criteria, theoretical considerations, and practical interpretability. Researchers may need to use their judgment and consider the context of their study when deciding on the final number of factors to retain in the EFA. Additionally, researchers may explore different factor solutions and compare their interpretability and consistency across multiple methods to ensure robustness in the factor structure.

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