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A Regression Equation for the Parallel Analysis Criterion in Principal Components Analysis: Mean and 95th Percentile
Multivariate Behavioral Research
|January 23, 2016
Summary
This study introduces a new regression equation for parallel analysis, improving the accuracy of determining the number of principal components in factor analysis. The equation predicts mean eigenvalues and 95th percentile values from random data, aiding component retention decisions.
Area of Science:
- Statistics
- Psychometrics
- Data Analysis
Background:
- Parallel analysis is a common Monte Carlo method for determining the number of factors or components.
- Existing methods may have limitations in accuracy and reliance on chance.
Purpose of the Study:
- To develop a more accurate regression equation for predicting parallel analysis values.
- To improve the decision-making process for retaining principal components in factor analysis.
Main Methods:
- Developed a regression equation using random data sets (5-50 variables, 50-500 subjects).
- Predicted mean eigenvalues and 95th percentile eigenvalues from random data matrices with unities in diagonals.
- Validated the equation's accuracy against previous methods.
Main Results:
- The new regression equation accurately predicts parallel analysis values (multiple correlations ≥ .95).
- It is more accurate than a previously published equation for predicting mean eigenvalues.
- The equation also effectively predicts the 95th percentile of eigenvalue distributions.
Conclusions:
- The proposed regression equation offers a more reliable tool for parallel analysis in principal components analysis.
- This enhances the accuracy of determining the optimal number of components to retain.
- Easy-to-use tables of regression weights are provided for practical application.
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