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A Sandwich Standard Error Estimator for Exploratory Factor Analysis With Nonnormal Data and Imperfect Models.

Guangjian Zhang1, Kristopher J Preacher2, Minami Hattori1

  • 1University of Notre Dame, IN, USA.

Applied Psychological Measurement
|June 26, 2019
PubMed
Summary

This study introduces a sandwich standard error (SE) estimator for exploratory factor analysis (EFA) to improve confidence intervals (CIs) with nonnormal data. The sandwich and bootstrap methods outperform the conventional information method for EFA under these conditions.

Keywords:
factor analysisfactor rotationlatent variable modelsstandard errors

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Data Analysis

Background:

  • Standard errors (SEs) and confidence intervals (CIs) are crucial for interpreting exploratory factor analysis (EFA) parameters.
  • Traditional methods may be inadequate when data are nonnormal or models are imperfect.

Purpose of the Study:

  • To adapt and evaluate a sandwich SE estimator for EFA parameters under various conditions, including nonnormal data and model misspecification.
  • To compare the performance of the sandwich method against conventional and bootstrap methods for SE and CI estimation in EFA.

Main Methods:

  • Adaptation of a sandwich SE estimator for EFA parameters.
  • Application to factor extraction using maximum likelihood and ordinary least squares.
  • Inclusion of various factor rotation methods (CF-varimax, CF-quartimax, geomin, target rotation).
  • Illustration with nonnormal continuous and ordinal data.
  • Comparison using simulated data with the information and bootstrap methods.

Main Results:

  • The adapted sandwich SE estimator effectively accommodates nonnormal data and imperfect models in EFA.
  • Both sandwich and bootstrap methods provided more satisfactory SE and CI estimates compared to the conventional information method.
  • The proposed methods demonstrated robustness in the presence of nonnormality and model approximation error.

Conclusions:

  • The sandwich SE method offers a more reliable approach for constructing confidence intervals in exploratory factor analysis, particularly with nonnormal data.
  • Researchers should consider the sandwich or bootstrap methods over the conventional information method for more accurate EFA results under challenging data conditions.