Flexible spatial modeling using copula with an application to water, sanitation and hygiene (wash) indicators in Namibia
Loading...
Date
2019
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
University of Namibia
Abstract
Spatial modelling is one approach that can serve as a basic tool in identifying areas that need intervention. Understanding the spatial distribution of indicators is of vital importance, as it help with national planning and decision-making. Different models such as Conditional Autoregressive (CAR) can be used in spatial modelling. However, these models pose analytic and statistical inferential challenges especially when non-continuous and multivariate response are involved. Therefore, a flexible approach such as copula can be used. Copula provides a flexible way to model multivariate outcomes by decomposing information from their joint distribution into that of its marginal distributions and defines the dependence structure. The approach is exemplified to analyze spatial distribution of Water, Sanitation and Hygiene (WASH) indicators. This study used a quantitative cross sectional study design using secondary data from the 2013 Namibia Demographic Health Survey (NDHS). The outcome variables used were water, sanitation and hygiene, while the covariates were; sex of household head, household size, age of the head of household, type of residence, wealth index, literacy, exposure to media, marital status, respondent occupations, working status and region. Two copula-based spatial modelling approaches were applied to model the discrete outcome variables. First, a Gaussian Copula Marginal Regression (GCMR) was used to estimate the spatial distribution of WASH indicators on geostatistical data. The fitting of GCMR models was done through the method of Maximum Likelihood Estimation (MLE). Secondly, a Generalized Joint Regression Modelling (GJRM) was used to model the joint spatial dependency of WASH indicators on areal data. The Markov Random Field (MRF) smoother was applied to the variable called region, while for continuous and discrete variables such as age and household size, the smooth functions were represented using the spline approach.
Results from the best GCMR model fitted showed that significant spatial disparities for improved drinking water, sanitation and hygiene exist at the regional level across Namibia. In addition, covariate such as sex, wealth index, education level, marital status, literacy, working status and residence were significant with respect to improved drinking water, sanitation and hygiene. Household size was significant to improved drinking water and hygiene, while age was significant to improved sanitation and hygiene. Improved drinking water was found to be low in Kavango, Ohangwena, Omusati and Kunene regions, while improved sanitation was low in Ohangwena and Zambezi regions. However, improved hygiene was much of a concern in Zambezi, Ohangwena, Oshana and Omusati regions.
For the joint model, the results indicated that residence and wealth index were significant to improved drinking water, hygiene and sanitation. It has been observed that there was a high positive correlation between the WASH indicators. In addition, the study has noticed that more regions were found to have a little spatial variation in improved drinking water.
Applying copula provided a flexible approach to the study in identifying areas that need major intervention for future improved drinking water, sanitation and hygiene. The presented maps and analysis approach demonstrated a mechanism for monitoring access to improved drinking water, sanitation and hygiene. It can also assist policy makers especially those involved in planning to develop comprehensive programmes and develop strategies for areas that were found to have low improved drinking water, sanitation and hygiene.
Description
A thesis submitted in partial fulfillment of the requirements for the Degree of Master of Science in Applied Statistics and Demography
Keywords
Copula, Sanitation, Hygiene