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A unified approach to exploratory factor analysis with missing data, nonnormal data, and in the presence of outliers

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Abstract

Factor analysis is regularly used for analyzing survey data. Missing data, data with outliers and consequently nonnormal data are very common for data obtained through questionnaires. Based on covariance matrix estimates for such nonstandard samples, a unified approach for factor analysis is developed. By generalizing the approach of maximum likelihood under constraints, statistical properties of the estimates for factor loadings and error variances are obtained. A rescaled Bartlett-corrected statistic is proposed for evaluating the number of factors. Equivariance and invariance of parameter estimates and their standard errors for canonical, varimax, and normalized varimax rotations are discussed. Numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures.

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Authors and Affiliations

  1. Laboratory for Social Research, University of Notre Dame, 919 Flanner Hall, 46556, Notre Dame, IN

    Ke-Hai Yuan

  2. University of North Texas, USA

    Linda L. Marshall

  3. University of California, Los Angeles

    Peter M. Bentler

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This project was supported by a University of North Texas Faculty Research Grant, Grant #R49/CCR610528 for Disease Control and Prevention from the National Center for Injury Prevention and Control, and Grant DA01070 from the National Institute on Drug Abuse. The results do not necessarily represent the official view of the funding agencies. The authors are grateful to three reviewers for suggestions that improved the presentation of this paper.

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Yuan, KH., Marshall, L.L. & Bentler, P.M. A unified approach to exploratory factor analysis with missing data, nonnormal data, and in the presence of outliers. Psychometrika 67, 95–121 (2002). https://doi.org/10.1007/BF02294711

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