Maximum likelihood estimation of Gaussian copula models for geostatistical count data

References

• Bai, Y., J. Kang, and P.-X. Song. 2014. Efficient pairwise composite likelihood estimation for spatial-clustered data. Biometrics 70 (3):661–70.
   PubMed Web of Science ®Google Scholar
• Baghishani, H., H. Rue, and M. Mohammadzadeh. 2012. On a hybrid data cloning method and its applications in generalized linear mixed models. Statistics and Computing 22 (2):597–613.
   Web of Science ®Google Scholar
• Baghishani, H., and M. Mohammadzadeh. 2011. A data cloning algorithm for computing maximum likelihood estimates in spatial generalized linear mixed models. Computational Statistics and Data Analysis 55 (4):1748–59.
   Web of Science ®Google Scholar
• Cameron, A. C., and P. K. Trivedi. 2013. Regression analysis of count data. 2nd ed. Cambridge: Cambridge University Press.
   Google Scholar
• Christensen, O. F., G. O. Roberts, and M. Sköld. 2006. Robust Markov chain Monte Carlo methods for spatial generalized linear mixed models. Journal of Computational and Graphical Statistics 15 (1):1–17.
   Web of Science ®Google Scholar
• De Oliveira, V. 2013. Hierarchical Poisson models for spatial count data. Journal of Multivariate Analysis 122:393–408.
   Web of Science ®Google Scholar
• Diggle, P. J., J. A. Tawn, and R. A. Moyeed. 2002. Model–based geostatistics (with discussion). Journal of the Royal Statistical Society: Series C (Applied Statistics) 47 (3):299–326.
   Web of Science ®Google Scholar
• Eddelbuettel, D., and C. Sanderson. 2014. RcppArmadillo: Accelerating R with high–performance C++ linear algebra. Computational Statistics and Data Analysis 71:1054–63.
   Web of Science ®Google Scholar
• Genz, A. 1992. Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics 1 (2):141–9.
   Google Scholar
• Genz, A., and F. Bretz. 2009. Computation of multivariate normal and t probabilities. Berlin: Springer.
   Google Scholar
• Genz, A., and F. Bretz. 2002. Comparison of methods for the computation of multivariate t–probabilities. Journal of Computational & Graphical Statistics 11 (4):950–71.
   Web of Science ®Google Scholar
• Geweke, J. 1991. Efficient simulation from the multivariate normal and student–t distributions subject to linear constraints. Computer Science and Statistics: Proceedings of the Twenty Third Symposium on the Interface, 571–578.
   Google Scholar
• Haario, H., E. Saksman, and J. Tamminen. 1999. Adaptive proposal distribution for random walk metropolis algorithm. Computational Statistics 14 (3):375–95.
   Web of Science ®Google Scholar
• Hajivassiliou, V., D. McFadden, and P. Ruud. 1996. Simulation of multivariate normal rectangle probabilities and their derivatives: Theoretical and computational results. Journal of Econometrics 72 (1–2):85–134.
   Web of Science ®Google Scholar
• Han, Z., and V. De Oliveira. 2018. gcKrig: An R package for the analysis of geostatistical count data using gaussian copulas. Journal of Statistical Software.
   Web of Science ®Google Scholar
• Han, Z., and V. De Oliveira. 2016. On the correlation structure of Gaussian copula models for geostatistical count data. Australian & New Zealand Journal of Statistics 58 (1):47–69.
   Web of Science ®Google Scholar
• Irvine, K., A. I. Gitelman, and J. A. Hoeting. 2007. Spatial designs and properties of spatial correlation: Effects on covariance estimation. Journal of Agricultural, Biological, and Environmental Statistics 12 (4):450–69.
   Web of Science ®Google Scholar
• Hickernell, F. J. 1998. A generalized discrepancy and quadrature error bound. Mathematics of Computation of the American Mathematical Society 67 (221):299–322.
   Web of Science ®Google Scholar
• Kazianka, H. 2013. Approximate copula–based estimation and prediction of discrete spatial data. Stochastic Environmental Research and Risk Assessment 27 (8):2015–26.
   Web of Science ®Google Scholar
• Kazianka, H., and J. Pilz. 2010. Copula–based geostatistical modeling of continuous and discrete data including covariates. Stochastic Environmental Research and Risk Assessment 24 (5):661–73.
   Web of Science ®Google Scholar
• Keane, M. P. 1994. A computationally practical simulation estimator for panel data. Econometrica 62 (1):95–116.
   Web of Science ®Google Scholar
• Knaus, J. 2015. snowfall: Easier Cluster Computing, R package version 1.84-6.1. http://cran.r-project.org/package=snowfall.
   Google Scholar
• Lele, S. R., K. Nadeem, and B. Schmuland. 2010. Estimability and likelihood inference for generalized linear mixed models using data cloning. Journal of the American Statistical Association 105 (492):1617–25.
   Web of Science ®Google Scholar
• Lele, S. R., B. Dennis, and F. Lutscher. 2007. Data cloning: Easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methods. Ecology Letters 10 (7):551–63.
   PubMed Web of Science ®Google Scholar
• Madsen, L. 2009. Maximum likelihood estimation of regression parameters with spatially dependent discrete data. Journal of Agricultural, Biological, and Environmental Statistics 14 (4):375–91.
   Web of Science ®Google Scholar
• Madsen, L., and Y. Fang. 2011. Joint regression analysis for discrete longitudinal data. Biometrics 67 (3):1171–6.
   PubMed Web of Science ®Google Scholar
• Masarotto, G., and C. Varin. 2017. Gaussian copula regression in R. Journal of Statistical Software 77 (8):1–26.
   Web of Science ®Google Scholar
• Masarotto, G., and C. Varin. 2012. Gaussian copula marginal regression. Electronic Journal of Statistics 6 (0):1517–49.
   Web of Science ®Google Scholar
• Meeker, W. Q., and L. A. Escobar. 1995. Teaching about approximate confidence regions based on maximum likelihood estimation. The American Statistician 49 (1):48–53.
   Web of Science ®Google Scholar
• Nikoloulopoulos, A. K. 2016. Efficient estimation of high–dimensional multivariate normal copula models with discrete spatial responses. Stochastic Environmental Research and Risk Assessment 30 (2):493–505.
   Web of Science ®Google Scholar
• Nikoloulopoulos, A. K. 2013. On the estimation of normal copula discrete regression models using the continuous extension and simulated likelihood. Journal of Statistical Planning and Inference 143 (11):1923–37.
   Web of Science ®Google Scholar
• Ponciano, J. M., M. L. Taper, B. Dennis, and S. R. Lele. 2009. Hierarchical models in ecology: Confidence intervals, hypothesis testing, and model selection using data cloning. Ecology 90 (2):356–62.
   PubMed Web of Science ®Google Scholar
• Sloan, I. H., and P. J. Kachoyan. 1987. Lattice methods for multiple integration: Theory, error analysis and examples. SIAM Journal on Numerical Analysis 24 (1):116–28.
   Web of Science ®Google Scholar
• Song, P. X. 2000. Multivariate dispersion models generated from Gaussian copula. Scandinavian Journal of Statistics 27 (2):305–20.
   Web of Science ®Google Scholar
• Thompson, E. A. 1994. Monte Carlo likelihoods in genetic mapping. Statistical Science 9 (3):355–66.
   Web of Science ®Google Scholar
• Torabi, M. 2015. Likelihood inference for spatial generalized linear mixed models. Communications in Statistics—Simulation and Computation 44 (7):1692–701.
   Web of Science ®Google Scholar
• Varin, C., N. Reid, and D. Firth. 2011. An overview of composite likelihood methods. Statistica Sinica 21:5–42.
   Web of Science ®Google Scholar
• Walker, A. M. 1969. On the asymptotic behavior of posterior distributions. Journal of the Royal Statistical Society B 31:80–8.
   Google Scholar
• Zhao, Y., and H. Joe. 2005. Composite likelihood estimation in multivariate data analysis. The Canadian Journal of Statistics 33 (3):335–56.
   Web of Science ®Google Scholar