### Abstract

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 assumptionson 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.

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 assumptionson 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.

Original language | English |
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Title of host publication | Machine Learning: ECML 2006 : 17th European Conference on Machine Learning. Berlin, Germany, September 2006. Proceedings |

Number of pages | 8 |

Publication date | 2006 |

Pages | 671-678 |

Publication status | Published - 2006 |

Event | European Conference on Machine Learning - Berlin, Germany Duration: 18 Sep 2006 → 22 Sep 2006 |

### Conference

Conference | European Conference on Machine Learning |
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Country | Germany |

City | Berlin |

Period | 18/09/2006 → 22/09/2006 |

### Fingerprint

### Cite this

Jaeger, M. (2006). On testing the missing at random assumption. In

*Machine Learning: ECML 2006: 17th European Conference on Machine Learning. Berlin, Germany, September 2006. Proceedings*(pp. 671-678)