Ordinary Least Squares Estimation of Parameters in Exploratory Factor Analysis With Ordinal Data

Area of Science:

• Social and behavioral sciences
• Psychometrics
• Statistical modeling

Background:

• Ordinal data, common in social sciences, is often inappropriately treated as continuous.
• Existing methods for exploratory factor analysis (EFA) with ordinal data have limitations.

Purpose of the Study:

• To propose and evaluate ordinary least squares (OLS) estimation for EFA using polychoric correlations.
• To provide standard errors and confidence intervals for parameter estimates in this context.

Main Methods:

• Estimation of polychoric correlations from ordinal data.
• Application of OLS to the EFA model specified on underlying continuous variables.
• Monte Carlo simulations to assess statistical properties.
• Empirical illustration with personality trait ratings.

Main Results:

• OLS estimation of EFA is feasible even for large models.
• Point estimates of rotated factor loadings are unbiased.
• Accurate standard errors and confidence intervals are provided.

Conclusions:

• The proposed OLS approach offers a viable method for EFA with ordinal data.
• This method enhances the analysis of complex psychological and social constructs.
• The findings support the use of OLS with polychoric correlations for robust EFA.