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Local computations of the iterative proportional scaling procedure for hierarchical models

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  • Xu, Ping-Feng
  • Sun, Jubo
  • Shan, Na

Abstract

The maximum likelihood estimation of hierarchical models for contingency tables is often carried out by the iterative proportional scaling (IPS) procedure. In this paper, we propose local computations of the IPS procedure by partitioning generators. The proposed implementation, called IPSP for short, first partitions generators into several non-overlapping and non-empty blocks, and then adjusts marginal counts in each block locally. To find an approximation to the optimal partition resulting the least complexity, we apply the simulated annealing algorithm. Moreover, local computations can speed up the implementation of the IPS procedure using junction trees. Numerical experiments are presented to illustrate the efficiency of local computations.

Suggested Citation

  • Xu, Ping-Feng & Sun, Jubo & Shan, Na, 2016. "Local computations of the iterative proportional scaling procedure for hierarchical models," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 17-23.
    • Handle: RePEc:eee:csdana:v:95:y:2016:i:c:p:17-23
    DOI: 10.1016/j.csda.2015.10.009
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    References listed on IDEAS

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    1. Gao, Wei & Shi, Ning-Zhong & Tang, Man-Lai & Fu, Lianyan & Tian, Guoliang, 2010. "Unified generalized iterative scaling and its applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1066-1078, April.
    2. Endo, Yushi & Takemura, Akimichi, 2009. "Iterative proportional scaling via decomposable submodels for contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 966-978, February.
    3. Badsberg, J. H. & Malvestuto, F. M., 2001. "An implementation of the iterative proportional fitting procedure by propagation trees," Computational Statistics & Data Analysis, Elsevier, vol. 37(3), pages 297-322, September.
    4. Jirousek, Radim & Preucil, Stanislav, 1995. "On the effective implementation of the iterative proportional fitting procedure," Computational Statistics & Data Analysis, Elsevier, vol. 19(2), pages 177-189, February.
    5. Roberts, G. O. & Smith, A. F. M., 1994. "Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms," Stochastic Processes and their Applications, Elsevier, vol. 49(2), pages 207-216, February.
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