Ordinary Least Squares Estimation of Parameters in Exploratory Factor Analysis With Ordinal Data
2012/03/30 by Chun-Ting Lee, Guangjian Zhang, Michael C. Edwards · 94 citations
Mathematics · #Advanced Statistical Methods and Models #Computer science #Data mining #Econometrics #Estimation #Exploratory data analysis #Exploratory factor analysis #Generalized least squares #Mathematics #Ordinal data #Ordinal optimization #Ordinal regression #Ordinary least squares #Statistical Methods and Inference #Statistical and numerical algorithms #Statistics #Structural equation modeling
paper · doi:10.1080/00273171.2012.658340
published in Multivariate Behavioral Research 47(2), 314-339 (Taylor & Francis)
openalex publication_date 2012/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
Abstract
Exploratory factor analysis (EFA) is often conducted with ordinal data (e.g., items with 5-point responses) in the social and behavioral sciences. These ordinal variables are often treated as if they were continuous in practice. An alternative strategy is to assume that a normally distributed continuous variable underlies each ordinal variable. The EFA model is specified for these underlying continuous variables rather than the observed ordinal variables. Although these underlying continuous variables are not observed directly, their correlations can be estimated from the ordinal variables. These correlations are referred to as polychoric correlations. This article is concerned with ordinary least squares (OLS) estimation of parameters in EFA with polychoric correlations. Standard errors and confidence intervals for rotated factor loadings and factor correlations are presented. OLS estimates and the associated standard error estimates and confidence intervals are illustrated using personality trait ratings from 228 college students. Statistical properties of the proposed procedure are explored using a Monte Carlo study. The empirical illustration and the Monte Carlo study showed that (a) OLS estimation of EFA is feasible with large models, (b) point estimates of rotated factor loadings are unbiased,
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