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Moderation analysis using a two-level regression model.

Ke-Hai Yuan1, Ying Cheng, Scott Maxwell

  • 1Department of Psychology, University of Notre Dame, Notre Dame, IN, 46556, USA, kyuan@nd.edu.

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Summary
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A new two-level regression model offers more accurate moderation analysis than traditional moderated multiple regression (MMR). This advanced method, using normal-distribution-based maximum likelihood (NML), improves parameter estimation, especially with heteroscedasticity.

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Area of Science:

  • Social and behavioral sciences
  • Statistical modeling

Background:

  • Moderation analysis is crucial in social and behavioral research.
  • Moderated multiple regression (MMR) using least squares (LS) is the common approach.
  • MMR models include product terms and are typically estimated by LS.

Purpose of the Study:

  • To propose and develop a two-level regression model for moderation analysis.
  • To provide an algorithm for parameter estimation using normal-distribution-based maximum likelihood (NML).
  • To compare the performance of the two-level model with MMR under different conditions.

Main Methods:

  • Developed a two-level regression model where regression coefficients are regressed on moderators.
  • Created an algorithm for parameter estimation using normal-distribution-based maximum likelihood (NML).
  • Derived and studied formulas for standard errors (SEs) of parameter estimates.

Main Results:

  • NML with the two-level model yields more efficient and accurate estimates than LS with MMR when heteroscedasticity is present.
  • NML with the two-level model produces similar results to LS with MMR under homoscedastic conditions.
  • The two-level model can estimate the percentage of variance in regression coefficients attributable to moderators.

Conclusions:

  • The two-level regression model with NML is a superior alternative to MMR for moderation analysis, particularly with heteroscedasticity.
  • This model offers enhanced accuracy and efficiency in parameter estimation.
  • The developed R package facilitates the practical application of this advanced statistical method.