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MCMC imputation in autologistic model

Author

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  • Zalewska Marta

    (Department of Environmental Hazards Prevention and Allergology, Medical University of Warsaw, Zwirki i Wigury 61, 02-091 Warszawa, Poland. E-mail:)

  • Niemiro Wojciech

    (Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland. E-mail:)

  • Samoliński Bolesław

    (Department of Environmental Hazards Prevention and Allergology, Medical University of Warsaw, Zwirki i Wigury 61, 02-091 Warszawa, Poland. E-mail:)

Abstract

We consider statistical inference from incomplete sets of binary data. Our approach is based on the autologistic model, which is very flexible and well suited for medical applications. We propose a Bayesian approach, essentially using Monte Carlo techniques. The method developed in this paper is a special version of Gibbs sampler. We repeat intermittently the following two steps. First, missing values are generated from the predictive distribution. Second, unknown parametes are estimated from the completed data. The Monte Carlo method of computing maximum likelihood estimates due to Geyer and Thompson (J. R. Statist. Soc. B 54: 657–699, 1992) is modified to the Bayesian setting and missing data problems. We include results of some small scale simulation experiments. We artificially introduce missing values in a real data set and then use our algorithm to refill missings. The rate of correct imputations is quite satisfactory.

Suggested Citation

  • Zalewska Marta & Niemiro Wojciech & Samoliński Bolesław, 2010. "MCMC imputation in autologistic model," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 421-438, January.
    • Handle: RePEc:bpj:mcmeap:v:16:y:2010:i:3-4:p:421-438:n:10
    DOI: 10.1515/mcma.2010.017
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    References listed on IDEAS

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    1. Little, Roderick J A, 1988. "Missing-Data Adjustments in Large Surveys," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 287-296, July.
    2. Little, Roderick J A, 1988. "Missing-Data Adjustments in Large Surveys: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 300-301, July.
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