Model Modification in Covariance Structure Modeling: A Comparison among Likelihood Ratio, Lagrange Multiplier, and...

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Covariance structure modeling is crucial for statistical analysis.
• Model comparisons traditionally rely on the likelihood ratio difference (D) test.
• The Lagrange Multiplier (LM) and Wald (W) tests offer alternative approaches.

Purpose of the Study:

• To empirically evaluate the performance of the D, LM, and W tests.
• To compare their effectiveness under null and alternative hypotheses.
• To assess their utility in covariance structure model modification.

Main Methods:

• Comparative analysis of three statistical tests: D, LM, and W.
• Empirical evaluation under various hypothesis conditions.
• Investigation of test behavior with different sample sizes.

Main Results:

• The LM and W tests demonstrate performance comparable to the D test at adequate sample sizes.
• The W test exhibited slight nonmonotonicity in its power function, which was not severe.
• The LM test, while generally behaving as expected, showed a tendency to over-parameterize under specific composite hypotheses, particularly with larger sample sizes.

Conclusions:

• The LM and W tests are viable alternatives to the D test for covariance structure modeling.
• A combined LM and W test strategy effectively corrects for the LM test's over-parameterization issue.
• This combined approach provides a robust method for covariance structure model modification.