Cheng, Chuchu. “Bootstrap Confidence Intervals of Fit Indexes”, Boston College, 2021. http://hdl.handle.net/2345/bc-ir:109088.
In SEM, fit indexes provide useful information about how well a hypothesized model fits the population. Bootstrap has been applied to construct confidence internals for fit indexes. We proposed the most recent method for constructing confidence intervals (CIs) of fit indexes (Cheng & Wu, 2017): the bootstrap-test-based method. This dissertation includes the most popular bootstrap CI methods and the bootstrap-test-based method. In addition to the percentile bootstrap CI method used in Zhang and Savalei (2016), we also included other popular bootstrap CI methods. For all bootstrap CI methods, we explored their performances with and without the transformation proposed by Yuan, Hayashi, and Yanagihara (2007). In this process, we also solved computation difficulty for Studentized CI. The bootstrap-test-based method is improved by using alternative search statistics. As the previous approaches were not extended to nonnormal conditions, the CI estimation for fit indexes with nonnormal data are investigated for both bootstrap CI and bootstrap-test-based methods, using adjusted definitions of fit indexes for nonnormal data. Different nonnormal data generation techniques are applied. This dissertation presents a comprehensive comparison of bootstrap CI methods and the bootstrap-test-based method under various conditions. From the simulation results, the CIs for fit indexes under the bootstrap-test-based method are more accurate than most bootstrap CI methods. The results also show that the bootstrap-test-based method can be generalized well to non-normal data. The confidence bounds coverage by bootstrap-test-based method are closer to their nominal levels.