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.

摘要

先前关于模型拟合卡方检验的自举p值的研究仅限于小型模型（大约 10 个变量），这表明如果样本量不太小，这些p值是准确的。对于小样本量（N  < 100），使用渐近方法获得的通常p值更准确。然而，随着变量数量的增加，渐近p值错误地表明模型拟合不佳。我们调查了 Bollen-Stine (1992) 自举p值是否可以使用正态和非正态数据克服这个问题。我们发现随着模型大小的增加，Bollen-Stine bootstrapped p与使用稳健方法（即均值和方差校正）获得的渐近p值相比，-值变得过于保守且准确度较低。不推荐使用Bollen-Stine p值来评估模型拟合。