Statistics and Its Interface

Volume 13 (2020)

Number 1

Nonparametric statistical inference and imputation for incomplete categorical data

Pages: 17 – 25

DOI: https://dx.doi.org/10.4310/SII.2020.v13.n1.a2

Authors

Chaojie Wang (Faculty of Science, Jiangsu University, Zhenjiang, China; and Department of Statistics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong)

Linghao Shen (Department of Information Engineering, Chinese University of Hong Kong, Shatin, N.T., Hong Kong)

Han Li (Department of Risk Management and Insurance, Shenzhen University, Shenzhen, China)

Xiaodan Fan (Department of Statistics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong)

Abstract

Missingness in categorical data is a common problem in various real applications. Traditional approaches either utilize only the complete observations or impute the missing data by some ad hoc methods rather than the true conditional distribution of the missing data, thus losing or distorting the rich information in the partial observations. In this paper, we propose the Dirichlet Process Mixture of Collapsed Product-Multinomials (DPMCPM) to model the full data jointly and compute the model efficiently. By fitting an infinite mixture of product-multinomial distributions, DPMCPM is applicable for any categorical data regardless of the true distribution, which may contain complex association among variables. Under the framework of latent class analysis, we show that DPMCPM can model general missing mechanisms by creating an extra category to denote missingness, which implicitly integrates out the missing part with regard to their true conditional distribution. Through simulation studies and a real application, we demonstrate that DPMCPM outperforms existing approaches on statistical inference and imputation for incomplete categorical data of various missing mechanisms. DPMCPM is implemented as the R package $\texttt{MMDai}$, which is available from the Comprehensive R Archive Network.

Keywords

infinite mixture model, product-multinomial distribution, missing data, imputation

The authors gratefully acknowledge three grants from the Research Grants Council of the Hong Kong SAR, China (400913, 14203915, 14173817) and two CUHK direct grants (4053135, 3132753).

Received 13 February 2019

Published 7 November 2019