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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  &lt; 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.

Asymptotic is Better than Bollen-Stine Bootstrapping to Assess Model Fit: The Effect of Model Size on the Chi-Square Statistic