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 at this https URL.

中文翻译：

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不完整分类数据的非参数统计推断和插补

分类数据中的缺失是各种实际应用中的常见问题。传统方法要么只利用完整的观察结果，要么通过一些特殊的方法来估算缺失数据，而不是缺失数据的真实条件分布，从而丢失或扭曲了部分观察中的丰富信息。在本文中，我们提出了折叠乘积多项式的狄利克雷过程混合（DPMCPM）来联合建模完整数据并有效地计算模型。通过拟合乘积多项分布的无限混合，DPMCPM 适用于任何分类数据，而不管真实分布如何，其中可能包含变量之间的复杂关联。在潜在类别分析的框架下，我们表明，DPMCPM 可以通过创建一个额外的类别来表示缺失，从而对一般缺失机制进行建模，该类别隐式地整合了缺失部分的真实条件分布。通过模拟研究和实际应用，我们证明 DPMCPM 在统计推断和估算各种缺失机制的不完整分类数据方面优于现有方法。DPMCPM 作为 R 包 \texttt{MMDai} 实现，可从综合 R 存档网络在此 https URL 获得。我们证明 DPMCPM 优于现有的统计推断和插补各种缺失机制的不完整分类数据的方法。DPMCPM 作为 R 包 \texttt{MMDai} 实现，可从综合 R 存档网络在此 https URL 获得。我们证明 DPMCPM 优于现有的统计推断和插补各种缺失机制的不完整分类数据的方法。DPMCPM 作为 R 包 \texttt{MMDai} 实现，可从综合 R 存档网络在此 https URL 获得。