Little’s MCAR test at different sample sizes

TLDR: Little’s MCAR test is unable to tell data that are MCAR from data that are MAR in small samples, but maintains the nominal error rate when null is true across a wide range of sample sizes.

I just found out about the R simglm package and decided to do a small simulation to test Little’s MCAR test¹ under different sample sizes. I could have investigated heteroskedasticity in linear regression instead, and I probably will in the future. I was able to find some examples of researchers using Little’s MCAR test at small sample sizes, so I ran a toy simulation.

And this is the script I used, the underlying regression is near perfect (no multicollinearity).