A Faster Procedure for Estimating CFA Models Applying Minimum Distance Estimators with a Fixed Weight Matrix

David Kreiberg, Katerina Marcoulides, Ulf Henning Olsson

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This paper presents a numerically more efficient implementation of the quadratic form minimum distance (MD) estimator with a fixed weight matrix for confirmatory factor analysis (CFA) models. In structural equation modeling (SEM) computer software, such as EQS, lavaan, LISREL and Mplus, various MD estimators are available to the user. Standard procedures for implementing MD estimators involve a one-step approach applying non-linear optimization techniques. Our implementation differs from the standard approach by utilizing a two-step estimation procedure. In the first step, only a subset of the parameters are estimated using non-linear optimization. In the second step, the remaining parameters are obtained using numerically efficient linear least squares (LLS) methods. Through examples, it is demonstrated that the proposed implementation of MD estimators may be considerably faster than what the standard implementation offer. The proposed procedure will be of particular interest in computationally intensive applications such as simulation, bootstrapping, and other procedures involving re-sampling.

Original languageEnglish (US)
Pages (from-to)725-739
Number of pages15
JournalStructural Equation Modeling
Issue number5
StatePublished - Dec 17 2020

Bibliographical note

Funding Information:
The authors would like to thank the reviewers for their insightful comments and suggestions in the course of preparing this text.

Publisher Copyright:
© 2020 Taylor & Francis Group, LLC.


  • CFA
  • estimation time
  • minimum distance estimator
  • quadratic form fit function


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