Filippou, Panagiota; (2018) Penalized Likelihood Estimation of Trivariate Additive Binary Models. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

In many empirical situations, modelling simultaneously three or more outcomes as well as their dependence structure can be of considerable relevance. Trivariate modelling is continually gaining in popularity (e.g., Genest et al., 2013; Król et al., 2016; Zhong et al., 2012) because of the appealing property to account for the endogeneity issue and non-random sample selection bias, two issues that commonly arise in empirical studies (e.g., Zhang et al., 2015; Radice et al., 2013; Marra et al., 2017; Bärnighausen et al., 2011). The applied and methodological interest in trivariate modelling motivates the current thesis and the aim is to develop and estimate a generalized trivariate binary regression model, which accounts for several types of covariate effects (such as linear, nonlinear, random and spatial effects), as well as error correlations. In particular, the thesis focuses on the following targets. First, we address the issue in estimating accurately the correlation coefficients, which characterize the dependence of the binary responses conditional on regressors. We found that this is not an unusual occurrence for trivariate binary models and as far as we know such a limitation is neither discussed nor dealt with. Based on this framework, we develop models for dealing with data suffering from endogeneity and/or nonrandom sample selection. Moreover, we propose trivariate Gaussian copula models where the link functions can in principle be derived from any parametric distribution and the parameters describing the association between the responses can be made dependent on several types of covariate effects. All the coefficients of the model are estimated simultaneously within a penalized likelihood framework based on a carefully structured trust region algorithm with integrated automatic multiple smoothing parameter selection. The developments have been incorporated in the function SemiParTRIV()/gjrm() in the R package GJRM (Marra & Radice, 2017). The extensive use of simulated data as well as real datasets illustrates each development in detail and completes the analysis.

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