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Sample-based Maximum Likelihood Estimation of the Autologistic Model

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  • S. Magnussen
  • R. Reeves

Abstract

New recursive algorithms for fast computation of the normalizing constant for the autologistic model on the lattice make feasible a sample-based maximum likelihood estimation (MLE) of the autologistic parameters. We demonstrate by sampling from 12 simulated 420×420 binary lattices with square lattice plots of size 4×4, …, 7×7 and sample sizes between 20 and 600. Sample-based results are compared with 'benchmark' MCMC estimates derived from all binary observations on a lattice. Sample-based estimates are, on average, biased systematically by 3%-7%, a bias that can be reduced by more than half by a set of calibrating equations. MLE estimates of sampling variances are large and usually conservative. The variance of the parameter of spatial association is about 2-10 times higher than the variance of the parameter of abundance. Sample distributions of estimates were mostly non-normal. We conclude that sample-based MLE estimation of the autologistic parameters with an appropriate sample size and post-estimation calibration will furnish fully acceptable estimates. Equations for predicting the expected sampling variance are given.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:5:p:547-561
    DOI: 10.1080/02664760701234967
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Katrin Dippold & Harald Hruschka, 2013. "Variable selection for market basket analysis," Computational Statistics, Springer, vol. 28(2), pages 519-539, April.
    4. Dippold, Katrin & Hruschka, Harald, 2010. "Variable Selection for Market Basket Analysis," University of Regensburg Working Papers in Business, Economics and Management Information Systems 443, University of Regensburg, Department of Economics.

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