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Abstract:
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This work investigates the computational efficiency in obtaining the maximum likelihood estimators of Gaussian copula models for geostatistical count data, where the likelihood can be expressed as high dimensional multivariate Gaussian integral. Two competitive simulated likelihood methods were selected and compared: the randomized quasi-Monte Carlo method in Genz and Bretz (2002), and the Geweke-Hajivassiliou-Keane (GHK) simulator. In addition, we formulated the Gaussian copula model hierarchically when the nugget effect is present in the latent Gaussian random field. The hierarchical formulation provides a way to use the data cloning (DC), a Markov chain Monte Carlo method that was initially used in the generalized linear mixed models, to circumvent the computation of the integral. A simpler pseudo-likelihood approach with two stage estimation procedure is also proposed. We conducted simulation study to assess performance of these four methods. Data example of tree counts in Lansing Woods was used to illustrate these methods.
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