Abstract
This work investigates the computation of maximum likelihood estimators in Gaussian copula models for geostatistical count data. This is a computationally challenging task because the likelihood function is only expressible as a high dimensional multivariate normal integral. Two previously proposed Monte Carlo methods are reviewed, the Genz–Bretz and Geweke–Hajivassiliou–Keane simulators, and a new method is investigated. The new method is based on the so–called data cloning algorithm, which uses Markov chain Monte Carlo algorithms to approximate maximum likelihood estimators and their (asymptotic) variances in models with computationally challenging likelihoods. A simulation study is carried out to compare the statistical and computational efficiencies of the three methods. It is found that the three methods have similar statistical properties, but the Geweke–Hajivassiliou–Keane simulator requires the least computational effort. Hence, this is the method we recommend. A data analysis of Lansing Woods tree counts is used to illustrate the methods.
Acknowledgements
We warmly thank two anonymous referees for helpful comments and suggestions that lead to an improved article.
Notes
1 With the convention that .