Testing MCAR via covariances: Extending the U-statistic framework to partially observed variables

Abstract

This paper presents a generalized version of a U-statistics-based test for MCAR developed by Aleksi\'c (2024). The proposed test, similar to the original, evaluates the MCAR assumption by calculating and combining the covariances between response indicators and data variables. However, unlike the preceding version, it is capable of utilizing partially observed variables, resulting in a significantly larger class of detectable alternatives. Numerical results indicate that the improved test is well-calibrated, notably outperforming the well-known MCAR test developed by Little (1988) used as a benchmark. For alternatives detectable by the original method, the improved test maintains comparable, although slightly lower, power, while consistently outperforming Little's test across all studied scenarios. For alternatives that were previously undetectable or marginally detectable, the novel test demonstrates the superior performance among the three methods. While the novel test shares the assumption of finite fourth moments of the data with Little's test, the results suggest it is more robust to this requirement, although both tests exhibit similar limitations.