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A method for bias-reduction of sample-based MLE of the autologistic model

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  • Magnussen, Steen
  • Reeves, Rob

Abstract

Sample-based maximum likelihood estimates (MLEI) of the autologistic function parameters obtained from a one-stage simple random cluster sample from a finite population of binary units on a regular grid are biased due to the neglected association between population units across cluster boundaries. This is because such estimates are based on the autologistic lattice of size corresponding to the sample cluster rather than that of the overall grid of interest. Considering a buffer of one row (column) of units around each sample cluster with 'missing data' and assuming independence of these buffered clusters permits a new set of maximum likelihood estimates (MLEB) after integrating out the missing data in the likelihood. MLEB are much less biased than MLEI and have much smaller root mean square errors. In a simulation study with square regular clusters with m={4,5,6,7} rows (columns) of units, sample sizes n={50,100,200}, and nine 420420 spatial fields with known values of the autologistic model parameters the buffering eliminated about 75% of the bias in MLEI and reduced root mean square errors accordingly. Achieved MLEB coverage rates of 95% confidence intervals were slightly conservative. We recommend buffering since it is easy to implement without adding significantly to computational efforts.

Suggested Citation

  • Magnussen, Steen & Reeves, Rob, 2008. "A method for bias-reduction of sample-based MLE of the autologistic model," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 103-111, September.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:1:p:103-111
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    References listed on IDEAS

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    1. A. N. Pettitt & N. Friel & R. Reeves, 2003. "Efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 235-246, February.
    2. Francesco Bartolucci, 2002. "A recursive algorithm for Markov random fields," Biometrika, Biometrika Trust, vol. 89(3), pages 724-730, August.
    3. R. Reeves, 2004. "Efficient recursions for general factorisable models," Biometrika, Biometrika Trust, vol. 91(3), pages 751-757, September.
    4. S. Magnussen & R. Reeves, 2007. "Sample-based Maximum Likelihood Estimation of the Autologistic Model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(5), pages 547-561.
    5. Michael L. Stein & Zhiyi Chi & Leah J. Welty, 2004. "Approximating likelihoods for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 275-296, May.
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    1. Jin, Ick Hoon & Liang, Faming, 2014. "Use of SAMC for Bayesian analysis of statistical models with intractable normalizing constants," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 402-416.
    2. Solaiman Afroughi & Soghrat Faghihzadeh & Majid Jafari Khaledi & Mehdi Ghandehari Motlagh & Ebrahim Hajizadeh, 2011. "Analysis of clustered spatially correlated binary data using autologistic model and Bayesian method with an application to dental caries of 3--5-year-old children," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2763-2774, February.

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