IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v27y2000i3p433-444.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9469.00199
    Download Restriction: no

    File URL: https://libkey.io/10.1111/1467-9469.00199?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:scjsta:v:27:y:2000:i:3:p:433-444. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.