Comparing the squared multiple correlation coefficients of non-nested models: an examination of confidence intervals...

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• Comparing non-nested models is crucial for selecting the best statistical model.
• Assessing predictor importance is fundamental in regression analysis.
• Existing methods for comparing squared multiple correlations have limitations.

Purpose of the Study:

• To investigate the performance of the asymptotic method for comparing squared multiple correlations in non-nested models.
• To evaluate the method's accuracy in determining predictor importance.
• To provide guidelines for sample size determination for hypothesis testing.

Main Methods:

• The study compared the increase in R2 when adding one predictor versus another within a regression model.
• The asymptotic method was applied to analyze these R2 changes.
• Simulations were likely used to assess performance across various sample sizes.

Main Results:

• The asymptotic procedure achieved expected coverage rates for sample sizes of 200 or more.
• Adequate statistical power often required substantially larger sample sizes than 200.
• The method's effectiveness is dependent on achieving sufficient power for hypothesis testing.

Conclusions:

• The asymptotic method is a viable approach for comparing non-nested models and assessing predictor importance.
• Careful consideration of sample size is necessary to ensure adequate power and reliable results.
• The study offers practical guidance for researchers on determining appropriate sample sizes for hypothesis testing in model comparisons.