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

Abstract

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.

Keywords:

• Categorical estimator
• missing data
• ordinal data
• robust estimator

Notes

¹ We focus on CFA models in this article for convenience though many of the issues discussed here are relevant to other SEMs.

² WLSMV is the default estimator in Mplus when categorical variables are declared; lavaan (Rosseel, 2012) in R (R Core Team, 2018) also automatically switches to WLSMV when it detects categorical variables.

³ Extremely large standard error (SE) estimates that fall outside of reasonable range suggest model convergence with numerical estimation problems. In practice, these improper solutions cannot be trusted and were therefore removed from subsequent analyses. We chose the proper range for SE to be 0–1 because SE cannot be negative, the true SEs (≤.48) are all well within this range, and the value of 1 would make at least one limit of all approximate 68% probable intervals for our parameters (standardized loadings and factor correlations) out of bound.