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A data cloning algorithm for computing maximum likelihood estimates in spatial generalized linear mixed models

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  • Baghishani, Hossein
  • Mohammadzadeh, Mohsen

Abstract

Non-Gaussian spatial data are common in many sciences such as environmental sciences, biology and epidemiology. Spatial generalized linear mixed models (SGLMMs) are flexible models for modeling these types of data. Maximum likelihood estimation in SGLMMs is usually made cumbersome due to the high-dimensional intractable integrals involved in the likelihood function and therefore the most commonly used approach for estimating SGLMMs is based on the Bayesian approach. This paper proposes a computationally efficient strategy to fit SGLMMs based on the data cloning (DC) method suggested by Lele et al. (2007). This method uses Markov chain Monte Carlo simulations from an artificially constructed distribution to calculate the maximum likelihood estimates and their standard errors. In this paper, the DC method is adapted and generalized to estimate SGLMMs and some of its asymptotic properties are explored. Performance of the method is illustrated by a set of simulated binary and Poisson count data and also data about car accidents in Mashhad, Iran. The focus is inference in SGLMMs for small and medium data sets.

Suggested Citation

  • Baghishani, Hossein & Mohammadzadeh, Mohsen, 2011. "A data cloning algorithm for computing maximum likelihood estimates in spatial generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1748-1759, April.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1748-1759
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    References listed on IDEAS

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    1. Jo Eidsvik & Sara Martino & Håvard Rue, 2009. "Approximate Bayesian Inference in Spatial Generalized Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 1-22, March.
    2. Varin, Cristiano & Host, Gudmund & Skare, Oivind, 2005. "Pairwise likelihood inference in spatial generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1173-1191, June.
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    8. repec:crs:wpaper:9320 is not listed on IDEAS
    9. Ole F. Christensen & Rasmus Waagepetersen, 2002. "Bayesian Prediction of Spatial Count Data Using Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 58(2), pages 280-286, June.
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    Cited by:

    1. Laurini Márcio Poletti, 2013. "A Hybrid Data Cloning Maximum Likelihood Estimator for Stochastic Volatility Models," Journal of Time Series Econometrics, De Gruyter, vol. 5(2), pages 193-229, May.
    2. Pedro Chaim & Márcio Poletti Laurini, 2022. "Data Cloning Estimation and Identification of a Medium-Scale DSGE Model," Stats, MDPI, vol. 6(1), pages 1-13, December.
    3. Anna Gottard & Giorgio Calzolari, 2014. "Alternative estimating procedures for multiple membership logit models with mixed effects: indirect inference and data cloning," Econometrics Working Papers Archive 2014_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    4. Baghishani, Hossein & Mohammadzadeh, Mohsen, 2012. "Asymptotic normality of posterior distributions for generalized linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 66-77.
    5. Picchini, Umberto & Anderson, Rachele, 2017. "Approximate maximum likelihood estimation using data-cloning ABC," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 166-183.

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