Little's MCAR test at different sample sizes

James Uanhoro

2017/09/21

Categories: stats rstats Tags: missing-data simulation small-samples

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.

Data are MCAR Data are MAR

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


  1. Little, R. J. A. (1988). A Test of Missing Completely at Random for Multivariate Data with Missing Values. Journal of the American Statistical Association, 83(404), 1198. https://doi.org/10.2307/2290157

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