Filippou Panagiota, Marra Giampiero, Radice Rosalba
Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, UK.
Department of Economics, Mathematics and Statistics, Birkbeck, University of London, Malet Street, London WC1E 7HX, UK.
Biostatistics. 2017 Jul 1;18(3):569-585. doi: 10.1093/biostatistics/kxx008.
This article proposes a penalized likelihood method to estimate a trivariate probit model, which accounts for several types of covariate effects (such as linear, nonlinear, random, and spatial effects), as well as error correlations. The proposed approach also addresses the difficulty in estimating accurately the correlation coefficients, which characterize the dependence of binary responses conditional on covariates. The parameters of the model are estimated within a penalized likelihood framework based on a carefully structured trust region algorithm with integrated automatic multiple smoothing parameter selection. The relevant numerical computation can be easily carried out using the SemiParTRIV() function in a freely available R package. The proposed method is illustrated through a case study whose aim is to model jointly adverse birth binary outcomes in North Carolina.
本文提出了一种惩罚似然方法来估计一个三变量概率单位模型，该模型考虑了几种类型的协变量效应（如线性、非线性、随机和空间效应）以及误差相关性。所提出的方法还解决了准确估计相关系数的困难，这些相关系数表征了二元响应在协变量条件下的依赖性。模型参数在一个惩罚似然框架内进行估计，该框架基于一种精心构建的信赖域算法，并集成了自动多重平滑参数选择。相关的数值计算可以使用一个免费的R包中的SemiParTRIV()函数轻松完成。通过一个案例研究对所提出的方法进行了说明，该案例研究的目的是联合模拟北卡罗来纳州不良出生二元结局。
