The effectiveness of weighted least squares means and variance adjusted based fit indices in assessing local dependence of the rasch model: Comparison with principal component analysis of residuals

Local independence is a principal assumption of applying latent variable models. Violations of this assumption might be stemmed from dimensionality (trait dependence) and statistical independence of item responses (response dependence). The purpose of this study is to evaluate the sensitivity of weighted least squares means and variance adjusted (WLSMV) based global fit indices to violations of local independence in Rasch models, and compare those indices to principal component analysis of residuals (PCAR) that is widely used for Rasch models. Dichotomous Rasch model is considered in this simulation study. The results show that WLSMV-based fit indices could detect trait dependence, but are to be limited with regard to response dependence. Additionally, WLSMV-based fit indices have advantages over the use of PCAR since WLSMV-based global fit indices are consistent regardless of sample size and test length. Though it is not recommended to apply exact benchmarks for those indices, they would provide practitioners with a method for evaluating the degree to which assumption violation is problematic for their data diagnostic purpose.