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Mixed Graphical Models with Missing Data and the Partial Imputation EM Algorithm

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  • Zhi Geng
  • Kang Wan
  • Feng Tao

Abstract

In this paper we discuss graphical models for mixed types of continuous and discrete variables with incomplete data. We use a set of hyperedges to represent an observed data pattern. A hyperedge is a set of variables observed for a group of individuals. In a mixed graph with two types of vertices and two types of edges, dots and circles represent discrete and continuous variables respectively. A normal graph represents a graphical model and a hypergraph represents an observed data pattern. In terms of the mixed graph, we discuss decomposition of mixed graphical models with incomplete data, and we present a partial imputation method which can be used in the EM algorithm and the Gibbs sampler to speed their convergence. For a given mixed graphical model and an observed data pattern, we try to decompose a large graph into several small ones so that the original likelihood can be factored into a product of likelihoods with distinct parameters for small graphs. For the case that a graph cannot be decomposed due to its observed data pattern, we can impute missing data partially so that the graph can be decomposed.

Suggested Citation

  • Zhi Geng & Kang Wan & Feng Tao, 2000. "Mixed Graphical Models with Missing Data and the Partial Imputation EM Algorithm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 433-444, September.
    • Handle: RePEc:bla:scjsta:v:27:y:2000:i:3:p:433-444
    DOI: 10.1111/1467-9469.00199
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    Cited by:

    1. Kuroda, Masahiro & Sakakihara, Michio, 2006. "Accelerating the convergence of the EM algorithm using the vector [epsilon] algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1549-1561, December.
    2. Geng, Zhi & Li, Kaican, 2003. "Factorization of posteriors and partial imputation algorithm for graphical models with missing data," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 369-379, October.
    3. Geng, Zhi & Wang, Chi & Zhao, Qiang, 2005. "Decomposition of search for v-structures in DAGs," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 282-294, October.
    4. Geng, Zhi & He, Yang-Bo & Wang, Xue-Li & Zhao, Qiang, 2003. "Bayesian method for learning graphical models with incompletely categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 175-192, October.
    5. Tang, Man-Lai & Wang Ng, Kai & Tian, Guo-Liang & Tan, Ming, 2007. "On improved EM algorithm and confidence interval construction for incomplete rxc tables," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2919-2933, March.
    6. Ng, Kai Wang & Tang, Man-Lai & Tan, Ming & Tian, Guo-Liang, 2008. "Grouped Dirichlet distribution: A new tool for incomplete categorical data analysis," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 490-509, March.

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