On Testing the Missing at Random Assumption

Most approaches to learning from incomplete data are based on the assumption that unobserved values are missing at random (mar). While the mar assumption, as such, is not testable, it can become testable in the context of other distributional assumptions, e.g. the naive Bayes assumption. In this paper we investigate a method for testing the mar assumption in the presence of other distributional constraints. We present methods to (approximately) compute a test statistic consisting of the ratio of two profile likelihood functions. This requires the optimization of the likelihood under no assumptions on the missingness mechanism, for which we use our recently proposed AI & M algorithm. We present experimental results on synthetic data that show that our approximate test statistic is a good indicator for whether data is mar relative to the given distributional assumptions.