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Multiplicity in multiple regression: Defining the issue, evaluating solutions, and integrating perspectives.

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Multiple hypothesis testing in regression increases error rates. This study evaluates ten multiple test procedures (MTPs) for regression, identifying effective methods to control familywise Type I error and enhance statistical power.

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Area of Science:

  • Statistics
  • Regression Analysis
  • Psychometrics

Background:

  • Familywise Type I error increases with multiple hypothesis tests.
  • Multiple test procedures (MTPs) control error rates but are underutilized in regression.
  • Existing research predominantly focuses on ANOVA, neglecting regression contexts.

Purpose of the Study:

  • Identify situations in multiple regression where multiplicity adjustment is crucial.
  • Evaluate the performance of ten MTPs in regression concerning error control and statistical power.
  • Integrate diverse perspectives on the advantages of multiplicity adjustment in regression.

Main Methods:

  • Simulation study investigating familywise Type I error control and statistical power.
  • Assessment of ten MTPs suitable for regression analysis.
  • Analysis of false discovery rate and simultaneous confidence intervals where applicable.

Main Results:

  • Multiple testing poses significant problems in regression, even in non-obvious scenarios.
  • Several MTPs demonstrated effective performance, especially those handling correlated parameters.
  • The magnitude of error inflation and method differences were quantified under plausible conditions.

Conclusions:

  • Multiplicity adjustment in regression is context-dependent and not universally required.
  • Specific MTPs offer balanced performance for controlling error rates and maintaining power.
  • Further research should consider contextual factors when deciding on multiplicity adjustments or alternative strategies.