Bernoulli amputation

TL;DR

This paper introduces a flexible method for modeling various missing data patterns using copulas and Bernoulli margins, enabling better handling of structured missingness in datasets.

Contribution

It presents a novel approach to simulate and analyze complex missing data patterns, including block and monotone missingness, using copula-based Bernoulli models.

Findings

Mathematically derived properties of missingness probabilities.

Demonstrated effectiveness with mathematical examples.

Empirical illustration on a well-known dataset.

Abstract

An approach to amputation, the process of introducing missing values to a complete dataset, is presented. It allows to construct missingness indicators in a flexible and principled way via copulas and Bernoulli margins and to incorporate dependence in missingness patterns. Besides more classical missingness models such as missing completely at random, missing at random, and missing not at random, the approach is able to model structured missingness such as block missingness and, via mixtures, monotone missingness, which are patterns of missing data frequently found in real-life datasets. Properties such as joint missingness probabilities or missingness correlation are derived mathematically. The approach is demonstrated with mathematical examples and empirical illustrations in terms of a well-known dataset.