Flexible MCAR testing for missing data with correlated response indicators

One of the most widely used tests for the missing completely at random (MCAR) assumption is Little’s test from 1988. However, as noted in 2024 by Aleksić, this test can suffer from substantial type I error distortion and loss of power when the data deviate from multivariate normality. Aleksić's test performs better under such departures, but it is limited to a very narrow class of detectable alternatives. Its subsequent generalization broadens the range of alternatives but introduces a new restriction: the response indicators must be uncorrelated. Here, we present a further generalization of this test that removes this assumption, and we compare its performance to both the original version and Little’s MCAR test.