Factor analyzing ordinal items requires substantive knowledge of response marginals

Area of Science:

• Social Sciences
• Psychometrics
• Statistical Modeling

Background:

• Ordinal measurement scales are prevalent in social sciences, often analyzed using factor analysis.
• Current methods either treat ordinal data as continuous or use discretization, with correlational analysis being central.
• Properly accounting for ordinal scales necessitates understanding item distributions or threshold spacing, often requiring substantive knowledge.

Approach:

• Review recent theories on correlations derived from ordinal data.
• Illustrate how a lack of substantive knowledge can lead to misinterpretations in factor analysis (e.g., a 2D case appearing as 1D).
• Investigate the impact of violating normality assumptions on correlations and factor models.

Key Points:

• Substantive knowledge (from expert insight, not just data) is crucial for accurate estimation in ordinal factor analysis.
• Ignoring item distributions or assuming equal thresholds can bias correlation and factor model results.
• An adjusted polychoric estimator is proposed to incorporate substantive knowledge.

Conclusions:

• The proposed adjusted polychoric estimator enhances the accuracy of ordinal factor analysis.
• This method offers a remedy for bias arising from unknown or approximate continuous item distributions.
• Sensitivity analysis using the adjusted estimator is demonstrated for situations with approximate distributional knowledge.