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Discrete responses in penalized Generalized Linear Models

Donat, F; (2016) Discrete responses in penalized Generalized Linear Models. Doctoral thesis , UCL (University College London). Green open access

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Abstract

Generalized Linear Models (GLMs) are an important class of models that provide a unifying framework for the analysis and estimation of several types response variables, including discrete outcomes. This thesis discusses the representation, estimation and some inferential results of various models for categorical responses within a penalized GLM structure. In particular, a ridge-type penalty form is included to enforce certain properties of the functional form of the covariate-response relationship. Specifically, fully, non-parametric effects as well as smoothed spatial dependencies are shown to be all be represented through an appropriate combination of linear predictors and penalisation terms. The emphasis of the thesis is on bivariate models for discrete responses that are commonly employed in cross-sectional studies to correct for the presence of direct unmeasured confounding and/or non-random sample selection issues. The former refers to a situation where both the response of interest and one of its relevant covariate are affected by a third variable, the confounder, which is either unobserved or not readily quantifiable by the researcher. The latter, instead, accounts for those instances where item non-response does not occur at random, but is driven by some underlying factors. In either case, not controlling for pertinent confounders may lead to detrimental effects in the estimates obtained, and standard estimators are usually inconsistent. Under certain conditions, bivariate models are proven to mend these issues. The thesis shows how both types of models can be represented within a unified penalized GLM framework for discrete responses. Methodological advances are then provided towards two main research avenues: (i) the estimation of non-parametric covariate effects and smoothed spatial dependencies, and (ii) an improved flexibility achieved through the specification of copula functions for the idiosyncratic model components. In this way, several alternative dependence structures among the responses are also introduced. The extensive use of real datasets illustrates each situation in details and completes the analysis.

Type: Thesis (Doctoral)
Title: Discrete responses in penalized Generalized Linear Models
Event: UCL (University College London)
Open access status: An open access version is available from UCL Discovery
Language: English
Keywords: Archimedean copulae, Bivariate system of equations, Ordinal responses, Penalized regression splines, Unobservables
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1493016
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