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Testing nonnested structural equation models.

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This study introduces Vuong's likelihood ratio tests for comparing nonnested structural equation models (SEMs). These tests, now accessible via R packages, provide a valuable tool for researchers evaluating different SEMs.

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Comparing nonnested structural equation models (SEMs) is challenging.
  • Existing methods for likelihood ratio tests in SEMs often require nonstandard output, limiting their application.
  • Previous applications have focused on mixture models.

Purpose of the Study:

  • To adapt and apply Vuong's (1989) likelihood ratio tests for comparing nonnested structural equation models (SEMs).
  • To demonstrate the construction of interval estimates for differences in nonnested information criteria.
  • To evaluate the performance and implementation of these tests in nonmixture SEMs.

Main Methods:

  • Application of Vuong's (1989) likelihood ratio tests.
  • Theoretical review of the underlying statistical principles.
  • Simulation studies to assess test performance.
  • Demonstration of implementation using free R packages.

Main Results:

  • The likelihood ratio tests are effective for comparing nonnested SEMs.
  • Interval estimates for differences in information criteria can be constructed.
  • The tests perform well in nonmixture SEM contexts.
  • Implementation is now straightforward using available R packages.

Conclusions:

  • Vuong's likelihood ratio tests provide a robust and accessible method for nonnested SEM comparison.
  • The removal of implementation barriers enhances their utility for researchers.
  • These tests offer a valuable tool for advancing quantitative research in various fields.