Applying the Bollen-Stine bootstrap for goodness-of-fit measures to structural equation models with missing data

The study proposed a method for extending the Bollen-Stine bootstrap of model fit to structural equation models with missing data. Matrix algebra difficulties associated with an incomplete data matrix are circumvented by applying the Bollen-Stine transformation to each case (or group of cases sharing a common pattern of missing data) using reduced arrays that contain elements corresponding to the observed variables. A SAS macro program is provided for the purposes of implementing this procedure, and its' performance was assessed in a simulation that varied distribution shape, sample size, and the missing data rate. Compared to the unadjusted fit statistic, which produced dramatically inflated Type I error rates, the bootstrap yielded model rejection rates quite close to the nominal 5% level, although rejection rates were conservative under small sample conditions.