Correct Point Estimator and Confidence Interval for RMSEA Given Categorical Data

Abstract

RMSEA estimation given nonnormal continuous data is usually based on the mean-adjusted () or mean-variance-adjusted () chi-square statistic, but a plain application of these statistics has poor performance. Savalei and colleagues gave a better way (the BSL method) to infer RMSEA using or . However, the BSL method is applicable to continuous data only. For categorical data, currently RMSEA inference is still based on a plain application of or , but such practice is already problematic under continuous data. In this paper, we first show that it is more meaningful to define RMSEA under unweighted least squares (ULS) than under weighted least squares (WLS) or diagonally weighted least squares (DWLS). Then, we propose a correct point estimator and confidence interval for RMSEA given categorical data and ULS. Simulation results show our methods perform well while all the traditional methods break down.