Corrected goodness-of-fit index in latent variable modeling using non-parametric bootstrapping

Latent variable modeling (LVM) is a powerful tool for validating tools and measurements in the social sciences. One of the main challenges in this method is the evaluation of model fit that is traditionally assessed using omnibus inferential statistical criteria, descriptive fit indices, and residual statistics, all of which are, to some extent, affected by sample sizes and model complexity. In the present study, an R function was created to assess fit indices after employing non-parametric bootstrapping. Furthermore, the newly proposed corrected goodness-of-fit index (CGFI) is presented as a means to overcome the abovementioned limitations. Using the data from Progress in International Student Assessment (PISA) 2022 and Progress in International Reading Literacy Study (PIRLS) 2021, the analysis of instructional leadership and the construct of bullying results revealed differential decision-making when using the present function compared to relying solely on sample estimates. It is suggested that the CGFIboot function may provide useful information toward improving our evaluative criteria in LVMs.