Penalized likelihood estimation of a trivariate additive probit model

Abstract

SUMMARY 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.

Copula selection models for non‐Gaussian outcomes that are missing not at random

“…Longitudinal settings typically pose further challenges to joint selection models as these often require additional parametric assumptions, for example, about the longitudinal correlation structure. Finally, the copula approach can be extended to settings that require joint inferences for more than one outcome (ie, beyond the bivariate copulae) . However, in typical health applications, such as the patient‐reported outcome measures illustrated in the REFLUX study, studies tend to focus on addressing non‐ignorability in a particular outcome .…”

Assessing the relationship between markers of glycemic control through flexible copula regression models

“…Other types of diagnostic criteria have also been defined by the ADA such as the two‐hour plasma glucose value during a 75‐g oral glucose tolerance test. We are also working on the development of regression models for trivariate copulas with a view to simultaneously study the effectiveness of these three criteria, in the line with the recent proposal of Filippou et al Preliminary results suggest that these approximations may help improve the diagnosis of diabetes.…”

A trivariate additive regression model with arbitrary link functions and varying correlation matrix

“…These include random, spatial and non-linear effects. We refer the reader to Filippou et al (2017), and references therein, for an overview of some common examples.…”

“…To minimize (5), we have extended the efficient and stable trust region algorithm with integrated automatic multiple smoothing parameter selection described by Filippou et al (2017) to allow for the specification of virtually any parametric link function, and for the correlation matrix to depend on covariate effects as described earlier. The practical success of these extensions depends on the availability of the analytical score and Hessian matrix of the model which are fundamental for a reliable, stable and efficient implementation of the above mentioned algorithm.…”

“…This paper contributes to the literature by introducing a generalization of the trivariate additive probit model. Specifically, we extend and therefore enhance the model proposed by Filippou et al (2017) by allowing (i) the link functions to be virtually derived from any parametric distribution and (ii) the model's association parameters to depend on several types of covariate effects (such as linear, nonlinear, random, and spatial effects). The first extension allows for the use of link functions other than probit.…”