Performance of Estimators for Confirmatory Factor Analysis of Ordinal Variables with Missing Data

Missing data and ordinal indicators are common in applied research involving latent constructs. Unfortunately, ordinal indicators violate the linearity assumption for conventional CFA that is routinely used to provide structural validity evidence for measurement instruments. Although robust maximum likelihood estimator (MLR) can deal with both missing data and nonnormality, it is generally inappropriate for ordinal indicators. Categorical estimation methods such as weighted least square mean and variance adjusted (WLSMV) method, or MLR or maximum likelihood (ML) that justly treats ordinal indicators as categorical (MLR-CAT or ML-CAT, respectively) have been recommended for ordinal dependent variables. However, performances of these categorical estimators in the presence of missing data have not been empirically examined. The current study systematically investigates the relative performances of WLSMV, MLR, MLR-CAT, and ML-CAT under different conditions of missing data amount and mechanism, sample size, level of indicator distribution, and number of indicator categories. Results generally favor MLR-CAT so long as the sample size is not too small (>200) to result in convergence problems.