Abstract

A Gaussian Copula-based regression model is proposed that accounts for associations between count responses with extra zeros. Our approach entails underlying latent variables to indicate the latent mechanisms which generate the count responses where some of the count responses are inflated in a zero point. The model contains, as special sub-models, several important distributions such as the power series distributions with and without extra zeros, for example, Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial distributions. The full likelihood-based inference method is applied for the estimation of parameters to obtain maximum likelihood estimates of the parameters. Modified Pearson residuals, where the correlation between responses is taken into account, are used for finding abnormal observations. To illustrate the utility of the models, some simulations are illustrated. Finally, the proposed models are applied to an insurance data set for insurers, obtained from an observational study, where the number of automobile claims and the number of third party claims are the correlated count responses. The effects of car age and the type of car, driving place on both responses are investigated simultaneously.

摘要

提出了一种基于高斯 Copula 的回归模型，该模型解释了计数响应与额外零之间的关联。我们的方法需要潜在的潜在变量来指示产生计数响应的潜在机制，其中一些计数响应在零点膨胀。作为特殊的子模型，该模型包含几个重要的分布，例如有和没有额外零的幂级数分布，例如泊松、负二项式、零膨胀泊松和零膨胀负二项式分布。完全基于似然的推理方法用于参数估计，以获得参数的最大似然估计。修改后的 Pearson 残差（其中考虑了响应之间的相关性）用于查找异常观察值。为了说明模型的效用，我们对一些模拟进行了说明。最后，将所提出的模型应用于保险公司的保险数据集，该数据集是从一项观察性研究中获得的，其中汽车索赔的数量和第三方索赔的数量是相关的计数响应。同时研究了汽车年龄和汽车类型、驾驶地点对这两种反应的影响。