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Approximate Maximum Likelihood Estimation of the Autologistic Model

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  • Marco Bee
  • Diego GIuliani
  • Giuseppe Espa

Abstract

Approximate Maximum Likelihood Estimation (AMLE) is a simple and general method recently proposed for approximating MLEs without evaluating the likelihood function. The only requirement is the ability to simulate the model to be estimated. Thus, the method is quite appealing for spatial models because it does not require evaluation of the normalizing constant, which is often computationally intractable. An AMLE-based algorithm for parameter estimation of the autologistic model is proposed. The impact of the numerical choice of the input parameters of the algorithm is studied by means of extensive simulation experiments, and the outcomes are compared to existing approaches. AMLE is much more precise, in terms of Mean-Square-Error, with respect to Maximum pseudo-likelihood, and comparable to ML-type methods. Although the computing time is non-negligible, the implementation is straightforward and the convergence conditions are weak in most practically relevant cases.
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Suggested Citation

  • Marco Bee & Diego GIuliani & Giuseppe Espa, 2013. "Approximate Maximum Likelihood Estimation of the Autologistic Model," DEM Discussion Papers 2013/12, Department of Economics and Management.
  • Handle: RePEc:trn:utwpem:2013/12
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    1. Luisa Corrado & Bernard Fingleton, 2012. "Where Is The Economics In Spatial Econometrics?," Journal of Regional Science, Wiley Blackwell, vol. 52(2), pages 210-239, May.
    2. Mark S. Kaiser & Petruţa C. Caragea, 2009. "Exploring Dependence with Data on Spatial Lattices," Biometrics, The International Biometric Society, vol. 65(3), pages 857-865, September.
    3. Ming Gao Gu & Hong‐Tu Zhu, 2001. "Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 339-355.
    4. Feizjavadian, S.H. & Hashemi, R., 2015. "Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 19-34.
    5. Giuseppe Arbia & Marco Bee & Giuseppe Espa, 2013. "Testing Isotropy in Spatial Econometric Models," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 228-240, September.
    6. Oecd, 1985. "OECD Declaration on Transborder Data Flows," OECD Digital Economy Papers 1, OECD Publishing.
    7. Fuchun Huang & Yosihiko Ogata, 2002. "Generalized Pseudo-Likelihood Estimates for Markov Random Fields on Lattice," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 1-18, March.
    8. D. R. Cox & Christiana Kartsonaki, 2012. "The fitting of complex parametric models," Biometrika, Biometrika Trust, vol. 99(3), pages 741-747.
    9. Giuseppe Arbia & Marco Bee & Giuseppe Espa, 2007. "Aggregation of regional economic time series with different spatial correlation structures," Department of Economics Working Papers 0720, Department of Economics, University of Trento, Italia.
    10. M. Sköld & G. O. Roberts, 2003. "Density Estimation for the Metropolis–Hastings Algorithm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 699-718, December.
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    Cited by:

    1. Bee, Marco & Benedetti, Roberto & Espa, Giuseppe, 2017. "Approximate maximum likelihood estimation of the Bingham distribution," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 84-96.
    2. Marco Bee & Roberto Benedetti & Giuseppe Espa, 2015. "Approximate likelihood inference for the Bingham distribution," DEM Working Papers 2015/02, Department of Economics and Management.

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