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The distributional transform (DT) is amongst the computational methods usedfor estimation of high-dimensional multivariate normal copula models withdiscrete responses. Its advantage is that the likelihood can be derivedconveniently under the theory for copula models with continuous margins, butthere has not been a clear analysis of the adequacy of this method. Weinvestigate the small-sample and asymptotic efficiency of the method forestimating high-dimensional multivariate normal copula models with univariateBernoulli, Poisson, and negative binomial margins, and show that the DTapproximation leads to biased estimates when there is more discretisation. Fora high-dimensional discrete response, we implement a maximum simulatedlikelihood method, which is based on evaluating the multidimensional integralsof the likelihood with randomized quasi Monte Carlo methods. Efficiencycalculations show that our method is nearly as efficient as maximum likelihoodfor fully specified high-dimensional multivariate normal copula models. Bothmethods are illustrated with spatially aggregated count data sets, and it isshown that there is a substantial gain on efficiency via the maximum simulatedlikelihood method.

Efficient estimation of high-dimensional multivariate normal copula models with discrete spatial responses