Regression modelling using priors depending on Fisher information covariance kernels (I-priors)

Regression analysis is undoubtedly an important tool to understand the relationship between one or more explanatory and independent variables of interest. In this thesis, we explore a novel methodology for fitting a wide range of parametric and nonparametric regression models, called the I-prior methodology (Bergsma, 2018). We assume that the regression function belongs to a reproducing kernel Hilbert or Kreĭn space of functions, and by doing so, allows us to utilise the convenient topologies of these vector spaces. This is important for the derivation of the Fisher information of the regression function, which might be infinite dimensional. Based on the principle of maximum entropy, an I-prior is an objective Gaussian process prior for the regression function with covariance function proportional to its Fisher information. Our work focusses on the statistical methodology and computational aspects of fitting I-priors models. We examine a likelihood-based approach (direct optimisation and EM algorithm) for fitting I-prior models with normally distributed errors. The culmination of this work is the R package iprior (Jamil, 2017) which has been made publicly available on CRAN. The normal I-prior methodology is subsequently extended to fit categorical response models, achieved by “squashing” the regression functions through a probit sigmoid function. Estimation of I-probit models, as we call it, proves challenging due to the intractable integral involved in computing the likelihood. We overcome this difficulty by way of variational approximations. Finally, we turn to a fully Bayesian approach of variable selection using I-priors for linear models to tackle multicollinearity. We illustrate the use of I-priors in various simulated and real-data examples. Our study advocates the I-prior methodology as being a simple, intuitive, and comparable alternative to similar leading state-of-the-art models

Pairwise likelihood estimation for confirmatory factor analysis models with categorical variables and data that are missing at random

Methods for the treatment of item non-response in attitudinal scales and in large-scale assessments under the pairwise likelihood (PL) estimation framework and under a missing at random (MAR) mechanism are proposed. Under a full information likelihood estimation framework and MAR, ignorability of the missing data mechanism does not lead to biased estimates. However, this is not the case for pseudo-likelihood approaches such as the PL. We develop and study the performance of three strategies for incorporating missing values into confirmatory factor analysis under the PL framework, the complete-pairs (CP), the available-cases (AC) and the doubly robust (DR) approaches. The CP and AC require only a model for the observed data and standard errors are easy to compute. Doubly-robust versions of the PL estimation require a predictive model for the missing responses given the observed ones and are computationally more demanding than the AC and CP. A simulation study is used to compare the proposed methods. The proposed methods are employed to analyze the UK data on numeracy and literacy collected as part of the OECD Survey of Adult Skills

Latent class analysis: insights about design and analysis of schistosomiasis diagnostic studies

Various global health initiatives are currently advocating the elimination of schistosomiasis within the next decade. Schistosomiasis is a highly debilitating tropical infectious disease with severe burden of morbidity and thus operational research accurately evaluating diagnostics that quantify the epidemic status for guiding effective strategies is essential. Latent class models (LCMs) have been generally considered in epidemiology and in particular in recent schistosomiasis diagnostic studies as a flexible tool for evaluating diagnostics because assessing the true infection status (via a gold standard) is not possible. However, within the biostatistics literature, classical LCM have already been criticised for real-life problems under violation of the conditional independence (CI) assumption and when applied to a small number of diagnostics (i.e. most often 3-5 diagnostic tests). Solutions of relaxing the CI assumption and accounting for zero-inflation, as well as collecting partial gold standard information, have been proposed, offering the potential for more robust model estimates. In the current article, we examined such approaches in the context of schistosomiasis via analysis of two real datasets and extensive simulation studies. Our main conclusions highlighted poor model fit in low prevalence settings and the necessity of collecting partial gold standard information in such settings in order to improve the accuracy and reduce bias of sensitivity and specificity estimates

Phytoremediation: treating euthrophic lake at kotasas lakeside, kuantan by aquatic macrophytes

This investigation was embraced ex-situ to investigate the capability of the submerged plants' water hyacinth (Eichornia crassipes) and water lettuce (Pistia stratiotes L.) as phytoremediation aquatic macrophytes for nutrients removal from a eutrophic lake situated at KotaSAS Lakeside surrounded by residential area as the risk of algae bloom can be avoided. The present of mankind activities such as sewage runoff and agricultural towards water bodies, the eutrophication process being speed up. The capability of these plants to evacuate certain parameters not just supplements while additionally including BOD5, COD, TSS, Turbidity, and heavy metals. The technique for investigation of lake water was alluded by Standard Method for Examination of Water and Wastewater. Water lettuce displayed extraordinary nitrate removal effectiveness up to 94% however this plant species shrivelled from week 2 of the examination because of an absence of nitrate supply and caused an expansion in phosphorus concentration. Then, water hyacinth indicates relentless evacuation productivity with a normal of 82% for nitrate and phosphorus. Other than that, water hyacinth indicates 88% and 72% of TSS and turbidity expulsion effectiveness which can improve the clarity of lake water. With this accomplishment gained in phytoremediation innovation utilizing water hyacinth, it is of most significance for this innovation to be executed in bigger scales in the future