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Model-implied simulation-based power estimation for correctly specified and distributionally misspecified models:

Julien P Irmer1, Andreas G Klein2, Karin Schermelleh-Engel2

  • 1Institute of Psychology, Department of Research Methods and Evaluation, Goethe University Frankfurt, Theodor-W.-Adorno-Platz 6, 60629, Frankfurt am Main, Germany. irmer@psych.uni-frankfurt.de.

Behavior Research Methods
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Summary
This summary is machine-generated.

This study introduces a new simulation-based method for power estimation in statistical testing. The model-implied simulation-based power estimation (MSPE) accurately determines sample sizes for desired statistical power across various models.

Keywords:
Distributional misspecificationModel misspecificationModerationNormality of parameter estimatesPowerSEMSimulation

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Area of Science:

  • Statistics
  • Statistical Modeling

Background:

  • Analytical power estimation is limited to specific models and requires correct specification.
  • Simulation-based power estimation is broadly applicable but lacks a general sample size calculation framework.

Purpose of the Study:

  • To propose a novel simulation-based power estimation method (MSPE) for the z-test.
  • To provide a general framework for calculating sample sizes for specified power rates.

Main Methods:

  • Developed a model-implied simulation-based power estimation (MSPE) method utilizing M-estimators and their asymptotic normality.
  • Employed a parametric model to link power and sample size for determining required sample sizes.
  • Evaluated performance in linear and nonlinear structural equation models (SEM) under correct and misspecified conditions.

Main Results:

  • The MSPE method demonstrated unbiasedness and good performance in terms of root mean squared error and type I error rates.
  • Predicted sample sizes and power rates showed high accuracy.
  • Outperformed alternative methods like linear interpolation and logistic regression.

Conclusions:

  • The MSPE method offers a widely applicable and accurate approach for power estimation, especially for models lacking analytical solutions.
  • It provides a valuable tool for determining sample sizes needed to achieve desired statistical power.