Testing Measurement Invariance with Ordinal Missing Data: A Comparison of Estimators and Missing Data Techniques

Abstract

Ordinal missing data are common in measurement equivalence/invariance (ME/I) testing studies. However, there is a lack of guidance on the appropriate method to deal with ordinal missing data in ME/I testing. Five methods may be used to deal with ordinal missing data in ME/I testing, including the continuous full information maximum likelihood estimation method (FIML), continuous robust FIML (rFIML), FIML with probit links (pFIML), FIML with logit links (lFIML), and mean and variance adjusted weight least squared estimation method combined with pairwise deletion (WLSMV_PD). The current study evaluates the relative performance of these methods in producing valid chi-square difference tests ($\Delta {\chi }^2$) and accurate parameter estimates. The result suggests that all methods except for WLSMV_PD can reasonably control the type I error rates of $\Delta {\chi }^2$ tests and maintain sufficient power to detect noninvariance in most conditions. Only pFIML and lFIML yield accurate factor loading estimates and standard errors across all the conditions. Recommendations are provided to researchers based on the results.

Keywords:

• Measurement invariance
• missing data
• ordinal data analysis