Using the Bollen-Stine Bootstrapping Method for Evaluating Approximate Fit Indices

Accepting that a model will not exactly fit any empirical data, global approximate fit indices quantify the degree of misfit. Recent research (Chen, Curran, Bollen, Kirby, & Paxton, 2008) has shown that using fixed conventional cut-points for approximate fit indices can lead to decision errors. Instead of using fixed cut points for evaluating approximate fit indices, this study focuses on the meaning of approximate fit and introduces a new method to evaluate approximate fit indices. Millsap (2012) introduced a simulation-based method to evaluate approximate fit indices. A limitation of Millsap's (2012) work was that a rather strong assumption of multivariate normality was implied in generating simulation data. In this study, the Bollen-Stine bootstrapping procedure (Bollen & Stine, 1993) is proposed to supplement the former study. When data are nonnormal, the conclusions derived from Millsap's (2012) simulation method and the Bollen-Stine method can differ. Examples are given to illustrate the use of the Bollen-Stine bootstrapping procedure for evaluating the Root Mean Squared Error of Approximation (RMSEA). Comparisons are made with the simulation method. The results are discussed, and suggestions are given for the use of proposed method.