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

The distributional transform (DT) is amongst the computational methods used for estimation of high-dimensional multivariate normal copula models with discrete responses. Its advantage is that the likelihood can be derived conveniently under the theory for copula models with continuous margins, but there has not been a clear analysis of the adequacy of this method. We investigate the small-sample and asymptotic efficiency of the method for estimating high-dimensional multivariate normal copula models with univariate Bernoulli, Poisson, and negative binomial margins, and show that the DT approximation leads to biased estimates when there is more discretisation. For a high-dimensional discrete response, we implement a maximum simulated likelihood method, which is based on evaluating the multidimensional integrals of the likelihood with randomized quasi Monte Carlo methods. Efficiency calculations show that our method is nearly as efficient as maximum likelihood for fully specified high-dimensional multivariate normal copula models. Both methods are illustrated with spatially aggregated count data sets, and it is shown that there is a substantial gain on efficiency via the maximum simulated likelihood method

An extended trivariate vine copula mixed model for meta-analysis of diagnostic studies in the presence of non-evaluable outcomes

A recent paper proposed an extended trivariate generalized linear mixed model (TGLMM) for synthesis of diagnostic test accuracy studies in the presence of non-evaluable index test results. Inspired by the aforementioned model we propose an extended trivariate vine copula mixed model that includes the TGLMM as special case, but can also operate on the original scale of sensitivity, specificity, and disease prevalence. The performance of the proposed vine copula mixed model is examined by extensive simulation studies in comparison with the TGLMM. Simulation studies showed that the TGLMM leads to biased meta-analytic estimates of sensitivity, specificity, and prevalence when the univariate random effects are misspecified. The vine copula mixed model gives nearly unbiased estimates of test accuracy indices and disease prevalence. Our general methodology is illustrated by meta-analysing coronary CT angiography studies

The bivariate K-finite normal mixture 'blanket' copula

There exist many bivariate parametric copulas to model bivariate data with different dependence features. We propose a new bivariate parametric copula family that cannot only handle various dependence patterns that appear in the existing parametric bivariate copula families, but also provides a more enriched dependence structure. The proposed copula construction exploits finite mixtures of bivariate normal distributions. The mixing operation, the distinct correlation and mean parameters at each mixture component introduce quite a flexible dependence. The new parametric copula is theoretically investigated, compared with a set of classical bivariate parametric copulas and illustrated on two empirical examples from astrophysics and agriculture where some of the variables have peculiar and asymmetric dependence, respectively

Weighted scores estimating equations and CL1 information criteria for longitudinal ordinal response

Available extensions of generalized estimating equations for longitudinal ordinal response require a conversion of the ordinal response to a vector of binary category indicators. That leads to a rather complicated working correlation structure and to large matrices when the number of categories and dimension of the clusters are large. Weighted scores estimating equations are constructed to overcome the aforementioned problems. Similar to generalized estimating equations which construct unbiased equations weighting the residuals, the weighted scores weight the univariate score functions. To specify the weight matrices, the weighted scores estimating equations use a working dependence model, namely the multivariate normal (MVN) copula model with univariate ordinal probit or logit regressions as the marginals. There is no need to convert the ordinal response to binary indicators, thus the weight matrices have smaller dimensions. Composite likelihood information criteria are further proposed as an intermediate step for selecting both the covariates in the mean function modelling and the structure of the latent correlation matrix induced by the MVN latent variables. The weighted scores estimating equations and composite likelihood information criteria are illustrated by analyzing a rheumatoid arthritis clinical trial. Our modelling framework is implemented in the package weightedScores within the open source statistical environment R