Asymptotic is Better than Bollen-Stine Bootstrapping to Assess Model Fit: The Effect of Model Size on the Chi-Square Statistic. Issue 5 (3rd September 2022) - Corrêa Ferraz, Raul; Maydeu-Olivares, Alberto; Shi, Dexin
Abstract: Previous research on bootstrapped p -values for the chi-square test of model fit has been limited to small models (around 10 variables), revealing that these p -values are accurate provided the sample size is not too small. For small sample sizes ( N  < 100), usual p -values, obtained using asymptotic methods, are more accurate. However, as the number of variables increases asymptotic p -values incorrectly suggest that models fit poorly. We investigate whether Bollen-Stine (1992) bootstrapped p -values can overcome this problem using normal and non-normal data. We found that as model size increases, Bollen-Stine bootstrapped p -values become too conservative and less accurate than asymptotic p -values obtained using robust methods (i.e., mean and variance corrections). Bollen-Stine p -values cannot be recommended to assess model fit.