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Determining the number of factors using parallel analysis and its recent variants
1Department of Psychology.
Psychological Methods
|June 11, 2019
Summary
Parallel analysis (PA) is a key method for determining the number of factors in statistical models. While traditional PA performs well, especially with population error, its accuracy decreases with low factor loadings, suggesting a flexible approach to factor number estimation.
Area of Science:
- Psychometrics
- Statistical analysis
- Factor analysis
Background:
- Parallel analysis (PA) is widely recommended for factor number determination.
- Theoretical justifications for PA, particularly eigenvalue use, have been questioned.
- Recent variants of PA aim to address these theoretical concerns.
Purpose of the Study:
- To discuss theoretical issues in using eigenvalues for dimensionality assessment.
- To review the development of PA and its variants.
- To evaluate the performance of different PA methods.
Main Methods:
- Monte Carlo simulation was employed to assess 13 PA variants.
- Simulations covered diverse factor structures and measurement scales.
- Performance was evaluated based on factor-representing and nonrepresenting eigenvalues.
Main Results:
- Traditional PA using full correlation matrices performed best under most conditions, particularly with population error.
- PA accuracy was unsatisfactory when factor loadings were low and factor correlations were high.
- Small factor-representing eigenvalues posed challenges for PA accuracy.
Conclusions:
- Original PA is recommended for factor number estimation.
- The estimated number of factors should not be treated as a fixed value.
- Consider a range of ±1 factor and consult interpretational validity for final decisions.
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