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Power analyses for measurement model misspecification and response shift detection with structural equation modeling.

M G E Verdam1,2

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Summary

This study provides examples and tools for calculating statistical power in structural equation modeling (SEM) to detect response shifts. This enhances the rigor of research examining changes in measurement meaning over time.

Keywords:
Chi-square testResponse shiftRoot mean square error of approximation (RMSEA)Sample size planningStatistical powerStructural equation modeling

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Quantitative Psychology

Background:

  • Statistical power is crucial for detecting response shifts using structural equation modeling (SEM).
  • Underreporting of power calculations in SEM for response shift detection limits research stringency.
  • Accessible methods for power analysis are needed to improve the quality of response shift research.

Purpose of the Study:

  • To address the underreporting of statistical power for response shift detection in SEM.
  • To provide worked-out examples and syntaxes for power calculations in SEM-based response shift detection.
  • To enhance the stringency of response shift research by facilitating power analysis uptake.

Main Methods:

  • Illustrated power calculations and sample-size requirements for detecting measurement model misspecification and response shifts.
  • Demonstrated step-by-step power analyses for hypotheses on overall model fit and response shift presence.
  • Utilized the R-package lavaan and the 'power4SEM' shiny-app for power calculations.

Main Results:

  • Showcased power calculations using the SF-36, including chi-square based power for model fit and response shift tests.
  • Demonstrated that a sample size of 506 is required to detect misspecification with medium cross-loadings.
  • Illustrated approximate fit power calculations using the RMSEA index.

Conclusions:

  • Provided accessible resources and emphasized distinct power analyses for different modeling goals.
  • Aimed to facilitate the adoption of power analyses for response shift detection in SEM.
  • Hoped to enhance the overall rigor and quality of response shift research.