# Model-based Clustering with Missing Not At Random Data

**Authors:** Aude Sportisse, Christophe Biernacki, Claire Boyer, Julie Josse, Matthieu Marbac Lourdelle, Gilles Celeux, Fabien Laporte  
**arXiv:** [2112.10425](https://arxiv.org/abs/2112.10425)  
**Date:** 2021-12-20  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2112.10425v1/

## Key points

- Technological advancements have led to the collection of vast amounts of data
- Model-based clustering is a popular methodology for exploring data within a statistical framework
- Missing values in large datasets pose a challenge for traditional approaches
- The paper addresses Missing Not At Random (MNAR) data, where missingness depends on observed and unobserved data values
- Authors propose an approach that integrates MNAR data into model-based clustering algorithms using a selection model
- The study investigates identifiability of parameters for various MNAR sub-models
- Estimation is done using EM and Stochastic EM algorithms to handle complexities introduced by missing not at random data
- Empirical evaluations on synthetic data sets validate the effectiveness of the proposed method
- Application on real-world medical data from TraumaBase dataset demonstrates potential impact in practical settings

## Summary

In recent years, the exponential growth of technological advancements has enabled the collection of vast amounts of data. Model-based clustering has emerged as a popular and versatile methodology for exploring data within a well-defined statistical framework. However, with the increase in large datasets, missing values have become more prevalent, posing a challenge for traditional approaches such as discarding observations with missing values or using imputation methods. This paper addresses the issue of Missing Not At Random (MNAR) data, where the missingness depends on both observed and unobserved data values. The authors propose a novel approach that integrates MNAR data directly into model-based clustering algorithms. They introduce a selection model that combines a mixture model for the data distribution with a general MNAR model for the missing-data mechanism. This model allows for dependencies on underlying classes and the values of missing variables, offering flexibility in handling complex missing data scenarios. The study derives a range of meaningful MNAR sub-models and investigates the identifiability of parameters for each sub-model—a crucial aspect in addressing MNAR scenarios. The estimation is carried out using EM (Expectation-Maximization) and Stochastic EM algorithms to handle the complexities introduced by missing not at random data. To validate their approach, empirical evaluations are conducted on synthetic data sets, demonstrating the effectiveness and relevance of the proposed method. Furthermore, the authors showcase its application on real-world medical data from the TraumaBase dataset, highlighting its potential impact in practical settings. Overall, this research contributes to advancing methodologies for handling missing not at random data within model-based clustering frameworks, offering insights into addressing challenges posed by incomplete datasets in modern statistical analysis.