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Profile Likelihood-Based Confidence Intervals and Regions for Structural Equation Models.

Jolynn Pek1, Hao Wu2

  • 1Department of Psychology, York University, 322 Behavioural Science Building, 4700 Keele Street, Toronto, ON, M3J 1P3 , Canada. pek@yorku.ca.

Psychometrika
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Summary
This summary is machine-generated.

This review compares Wald-type and likelihood-based methods for interval estimation in structural equation models (SEM). Profile likelihood methods offer robust confidence intervals and regions for complex SEM analyses.

Keywords:
Waldconfidence intervalsconfidence regionsmulti-parameterprofile likelihood

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Structural Equation Models (SEM) are essential for analyzing complex multivariate relationships.
  • Existing interval estimation methods in SEM lack a comprehensive review.
  • Accurate interval estimation is crucial for reliable SEM results.

Purpose of the Study:

  • To provide a comprehensive review of interval estimation methods in linear SEM.
  • To emphasize and detail profile likelihood-based confidence intervals (CIs) and confidence regions (CRs).
  • To offer practical guidance on selecting appropriate estimation methods.

Main Methods:

  • Review of popular Wald-type interval estimation methods.
  • Detailed examination of likelihood-based methods, particularly profile likelihood.
  • Description of algorithms for computing profile likelihood-based CIs and CRs.
  • Illustration using empirical examples and OpenMx code.

Main Results:

  • Profile likelihood-based methods provide valuable alternatives to Wald-type methods for SEM.
  • New algorithms enhance the construction of profile likelihood-based CIs and CRs.
  • Empirical examples demonstrate the practical application of these methods.

Conclusions:

  • Profile likelihood-based confidence intervals and regions are recommended for complex SEM.
  • Understanding the strengths and weaknesses of different methods aids in choosing the best approach.
  • Practical guidelines are provided for researchers using SEM.