A Simple Analytic Confidence Interval for CFI Given Nonnormal Data

The comparative fit index (CFI) is one of the most widely-used fit indices in structural equation modeling (SEM). When applying the CFI to model evaluation, although it is universally recognized that the focus should be the population fit, in practice one often considers only the CFI value within a sample and neglects the uncertainty in point estimation. Confidence interval (CI) methods for CFI appeared only recently, but these methods assume multivariate normality, which often fails to hold in practice. In addition, the current methods are applications of the bootstrap and are thus computationally intensive. To better handle nonnormal data and simplify CI construction, in this paper we propose an analytic CI method for CFI without assuming normality. We then carry out simulation studies to compare the new and current methods at various levels of model misfit and nonnormality. Simulation results verify the effectiveness and advantages of the new method.