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

Chun Ting Lee, Guangjian Zhang, Michael Edwards

Research output: Contribution to journalArticle

27 Citations (Scopus)

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, (c) point estimates of factor correlations are slightly negatively biased with small samples, and (d) standard error estimates and confidence intervals perform satisfactorily at moderately large samples.

Original languageEnglish (US)
Pages (from-to)314-339
Number of pages26
JournalMultivariate Behavioral Research
Volume47
Issue number2
DOIs
StatePublished - Mar 1 2012
Externally publishedYes

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Ordinal Variables
Exploratory Factor Analysis
Ordinal Data
Ordinary Least Squares
Least Squares Estimation
Least-Squares Analysis
Statistical Factor Analysis
Continuous Variables
Polychoric Correlation
Standard error
Confidence interval
Point Estimate
Confidence Intervals
Monte Carlo Study
Error Estimates
Behavioral Sciences
Least Squares Estimate
Social Sciences
Small Sample
Statistical property

ASJC Scopus subject areas

  • Statistics and Probability
  • Experimental and Cognitive Psychology
  • Arts and Humanities (miscellaneous)

Cite this

Ordinary Least Squares Estimation of Parameters in Exploratory Factor Analysis With Ordinal Data. / Lee, Chun Ting; Zhang, Guangjian; Edwards, Michael.

In: Multivariate Behavioral Research, Vol. 47, No. 2, 01.03.2012, p. 314-339.

Research output: Contribution to journalArticle

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