Old and new ideas for data screening and assumption testing for exploratory and confirmatory factor analysis

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Factor analysis traditionally models continuous variables using linear regression principles.
• Modern applications often involve analyzing individual items, which are frequently categorical (e.g., Likert-type).
• Product-moment correlations may inadequately represent relationships in categorical item data.

Purpose of the Study:

• To review data screening and assumption testing for factor analysis.
• To provide practical advice for handling continuous and categorical variables in factor analysis.
• To highlight the importance of appropriate methods for item-level factor analysis.

Main Methods:

• Review of assumptions for the common factor model with continuous variables.
• Application of regression diagnostics principles to factor analysis.
• Discussion of non-linear factor analysis and polychoric correlations for categorical data.
• Demonstration using a historical cognitive ability data set.

Main Results:

• Traditional linear factor analysis assumptions are detailed for continuous data.
• Challenges with analyzing categorical item data using standard methods are identified.
• Non-linear factor analysis with polychoric correlations is presented as a viable alternative for item analysis.

Conclusions:

• Appropriate data screening and assumption testing are critical for valid factor analysis.
• Researchers must consider variable type (continuous vs. categorical) when selecting factor analysis methods.
• Non-linear factor analysis offers a robust approach for questionnaire item data.