Bollen-Stine Bootstrapping of the Chi-Square Statistic in Structural Equation Models: The Effect of Model Size
Date of Award
Open Access Thesis
Previous research on the accuracy of p-values for the chi-square test of model fit has been limited to small models (around 10 variables), revealing that they are accurate provided sample size is not too small. At small sample sizes (N < 100), the usual p-values, obtained using asymptotic methods, are more accurate. However, asymptotic p-values incorrectly suggest that models fit poorly when the number of variables is large. We investigate whether Bollen-Stine (1992) bootstrap p-values are accurate in large models (up to 30 variables) for continuous outcomes using both normal and non-normal data. We found that as model size increases bootstrap p-values become too conservative (rejection rates are too small) and remarkably less accurate than asymptotic p-values obtained using robust methods (i.e., mean and variance corrected chi-square statistics). Further, there is a significant interaction between model size and sample size such that p-values for bootstrap are less accurate when the model is large and the sample size is small. Bollen-Stine p-values cannot be recommended to assess the fit of large models.
Corrêa Ferraz, R.(2020). Bollen-Stine Bootstrapping of the Chi-Square Statistic in Structural Equation Models: The Effect of Model Size. (Master's thesis). Retrieved from https://scholarcommons.sc.edu/etd/6074