Dear colleagues
As far as I know that the screeplot n Principal Axis Factoring (PAF) represents the eigenvalues and number of factors in the initial and not the extraction solution.
Since the eigenvalues in the initial and the extraction eigenvalues differ from each other, can I still use the screeplot to identify the number of factors extracted or it will be misleading?
Thank you
The scree plot is a graphical method to determine the number of factors to retain in factor analysis. It shows the eigenvalues of the factors or components on the y-axis and the number of factors or components on the x-axis. The scree plot usually displays a downward curve, and the point where the curve levels off (the “elbow”) is used to identify the optimal number of factors or components to retain.
However, the scree plot can be misleading when applied to principal axis factoring (PAF), because it shows the eigenvalues of the initial correlation matrix, not the reduced correlation matrix after extracting the factors. The initial eigenvalues are based on the assumption that all variables are perfectly measured, while the reduced eigenvalues are based on the estimated communalities that reflect the measurement error. Therefore, the initial eigenvalues tend to be larger than the reduced eigenvalues, and the scree plot may overestimate the number of factors to retain.
To avoid this problem, some researchers suggest using a modified scree plot that shows the reduced eigenvalues instead of the initial eigenvalues. This can be done by using a software program that can output the reduced eigenvalues, such as SPSS or R. Alternatively, some researchers suggest using other methods to determine the number of factors to retain, such as parallel analysis, minimum average partial correlation, or Velicer’s MAP test. These methods are more objective and reliable than the scree plot.
Some references that provide more details about the scree plot and PAF are:
- Scree plot - Wikipedia1
- r - How to create a scree plot for factor analysis given that eigenvalues depend on the number of extracted factors? - Cross Validated2
- Factor Analysis Extraction - IBM3
- Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99(3), 432–442.
https://en.wikipedia.org/wiki/Scree_plot
https://stats.stackexchange.com/questions/241032/how-to-create-a-scree-plot-for-factor-analysis-given-that-eigenvalues-depend-on
https://www.ibm.com/docs/en/spss-statistics/saas?topic=analysis-factor-extraction
https://sanchitamangale12.medium.com/scree-plot-733ed72c8608
Good luck
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