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A Cross-Entropy approach to the estimation of Generalised Linear Multilevel Models

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  • Marco Bee
  • Giuseppe Espa
  • Diego Giuliani
  • Flavio Santi

Abstract

In this paper we use the cross-entropy method for noisy optimisation for fitting generalised linear multilevel models through maximum likelihood. We propose specifications of the instrumental distributions for positive and bounded parameters that improve the computational performance. We also introduce a new stopping criterion, which has the advantage of being problem-independent. In a second step we find, by means of extensive Monte Carlo experiments, the most suitable values of the input parameters of the algorithm. Finally, we compare the method to benchmark estimation technique based on numerical integration. The cross-entropy approach turns out to be preferable from both the statistical and the computational point of view. In the last part of the paper, the method is used to model death probability of firms in the healthcare industry in Italy.

Suggested Citation

  • Marco Bee & Giuseppe Espa & Diego Giuliani & Flavio Santi, 2015. "A Cross-Entropy approach to the estimation of Generalised Linear Multilevel Models," DEM Working Papers 2015/04, Department of Economics and Management.
    • Handle: RePEc:trn:utwprg:2015/04
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    References listed on IDEAS

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    1. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    2. Rubinstein, Reuven Y., 1997. "Optimization of computer simulation models with rare events," European Journal of Operational Research, Elsevier, vol. 99(1), pages 89-112, May.
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    Cited by:

    1. Marco Bee & Maria Michela Dickson & Diego Giuliani & Davide Piacentino & Flavio Santi & Emanuele Taufer, 2016. "La sopravvivenza immediata delle start-up italiane del settore manifatturiero sanitario: un?analisi multilevel," RIVISTA DI ECONOMIA E STATISTICA DEL TERRITORIO, FrancoAngeli Editore, vol. 2016(3), pages 49-59.

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