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Determining the Number of Factors When Population Models Can Be Closely Approximated by Parsimonious Models
1University of Illinois at Urbana-Champaign, Champaign, IL, USA.
Educational and Psychological Measurement
|September 27, 2021
Summary
Traditional parallel analysis (TPA) is recommended for determining the number of factors in behavioral research. It shows higher accuracy, especially when models closely approximate population data with minor misfits.
Area of Science:
- Psychometrics
- Behavioral Science
- Statistical Modeling
Background:
- Determining the correct number of factors is crucial in factor analysis.
- Existing methods lack universal applicability across all research conditions.
Purpose of the Study:
- To compare the performance of various factor determination methods under realistic behavioral research scenarios.
- To evaluate method accuracy when a K-factor model closely approximates population data with trivial model-data misfit.
Main Methods:
- Comparison of Traditional Parallel Analysis (TPA), Revised Parallel Analysis (RPA), Kaiser's rule, Minimum Average Partial, and sequential fit indices (χ², RMSEA, CFI, TLI).
- Simulation study under conditions with and without population-level misfits.
Main Results:
- TPA and RPA perform well with zero population misfits.
- RPA accuracy significantly decreases with trivial model-data misfit.
- TPA demonstrates the least sensitivity to trivial misfits and highest overall accuracy.
Conclusions:
- Traditional Parallel Analysis (TPA) is suggested for the investigated models in behavioral studies.
- Revised Parallel Analysis (RPA) may require further development to handle acceptable levels of model-data misfit.
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