Accuracy in Parameter Estimation for the Root Mean Square Error of Approximation: Sample Size Planning for Narrow...

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Structural equation modeling (SEM) frequently uses the root mean square error of approximation (RMSEA) to assess model fit.
• Confidence intervals for RMSEA are crucial for interpreting the precision of this fit measure.

Purpose of the Study:

• To develop a sample size planning approach for RMSEA based on accuracy in parameter estimation.
• To ensure the expected width of the confidence interval for the population RMSEA is sufficiently narrow.

Main Methods:

• Developed analytic methods for sample size planning targeting RMSEA confidence interval width.
• Utilized Monte Carlo simulation to validate the analytic developments.
• Created freely available computer software for practical implementation.

Main Results:

• Analytic methods for sample size planning demonstrated effectiveness in simulations.
• The developed approach successfully targets a narrow expected confidence interval width for RMSEA.
• Software implementation facilitates the application of these methods.

Conclusions:

• The proposed accuracy in parameter estimation approach provides a robust method for sample size planning in SEM when RMSEA is of interest.
• This method enhances the precision of model fit assessment by ensuring narrow confidence intervals.
• The study provides practical tools for researchers to determine adequate sample sizes for their SEM analyses.