A holistic Bayesian framework for modelling latent socio-economic health

Abstract

This thesis details two related research projects. First, we develop a model-based LAtent Causal Socioeconomic Health (LACSH) index at the national level using hierarchical latent variable, spatial and causal modelling. Second, we propose methods based on the extended rank likelihood method to jointly model multiple treatment causal variables of various types including binary, ordinal and continuous. In the first project, we conduct two global case studies on national socioeconomic health (latent trait) with our LACSH approach. The second project introduces the National Medical Expenditure Survey (NMES) data from the USA only. In both projects, countries' data are collated from various organisations. All of our approaches are structured and implemented in a Bayesian framework and results are obtained by Markov chain Monte Carlo techniques.

The main project of this thesis (Chapters 2-4) is on developing the integrated LACSH framework to facilitate the understanding of how observational binary and continuous variables might have causally affected a latent trait that exhibits spatial correlation. In Chapter 2, we review the methods of the existing wellbeing indices available, and introduce the countries' data used in the two global case studies. These data feature various metrics and covariates pertaining to different aspects of societal health, and the policy (treatment) variable being mandatory maternity leave days and government expenditure on healthcare, respectively. In Chapter 3, we describe the building blocks for our LACSH framework and index. The framework is built upon the latent health factor index (LHFI) approach that has been used to assess the unobservable ecological/ecosystem health. We integrate the LHFI structure with spatial modelling and statistical causal modelling. For the causal modelling structure, we first consider propensity score methods for a binary policy variable and extend it to the case of a continuous treatment. A novel visualisation technique for evaluating covariate balance is also introduced for the case of a continuous policy variable. In Chapter 4, we illustrate our resulting LACSH framework and visualisation tool through the two case studies.

The second project of the thesis focuses on the latent-health level and the treatment level of the LACSH framework. It is discussed in Chapter 5, where we propose a semiparametric approach that incorporates an extended rank likelihood method with the estimation of the propensity score. This is to facilitate joint modelling of diverse types of treatment variables that may include continuous, binary, and ordinal. This can lead to two definitions of the propensity score: one applied to the rank-based parameters for the treatment and covariates in the extended rank likelihood ("latent version"), and the other being the traditional definition that utilises the treatment and covariates directly ("non-latent version"). After we introduce the NMES data, we apply two variants of our proposed approach of this Chapter, which we term the Latent Propensity Function (LPF) and the Latent Generalised Propensity Score (LGPS), to both the NMES data and those from the first project in Chapters 2-4. We assess the performance between the latent and non-latent versions.

In the final chapter of this thesis, Chapter 6, we summarise our work and discuss some potential future work.