Spatial-Longitudinal Bent-Cable Model with an Application to Atmospheric CFC Data

Spatial data (also called georeferenced data) arise in a wide range of scientific studies, including geography, agriculture, criminology, geology, urban and regional economics. The underlying spatial effects – the measurement error caused by any spatial pattern embedded in data – may affect both the validity and robustness of traditional descriptive and inferential techniques. Therefore, it is of paramount importance to take into account spatial effects when analysing spatially dependent data. In particular, addressing the spatial association among attribute values observed at different locations and the systematic variation of phenomena by locations are the two major aspects of modelling spatial data. The bent-cable is a parametric regression model to study data that exhibits a trend change over time. It comprises two linear segments to describe the incoming and outgoing phases, joined by a quadratic bend to model the transition period. For spatial longitudinal data, measurements taken over time are nested within spatially dependent locations. In this thesis, we extend the existing longitudinal bent-cable regression model to handle spatial effects. We do so in a hierarchical Bayesian framework by allowing the error terms to be correlated across space. We illustrate our methodology with an application to atmospheric chlorofluorocarbon (CFC) data. We also present a simulation study to demonstrate the performance of our proposed methodology. Although we have tailored our work for the CFC data, our modelling framework may be applicable to a wide variety of other situations across the range of the econometrics, transportation, social, health and medical sciences. In addition, our methodology can be further extended by taking into account interaction between temporal and spatial effects. With the current model, this could be done with a spatial correlation structure that changes as a function of time.

Name thesis:degree_name

Master of Science (M.Sc.)

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Saskatchewan

Year dc:date.issued

2012

Author dc:creator

• Rana, Md Masud

Advisors dc:contributor.advisor

• Khan, Shahedul A.
• Li, Longhai

Committee members dc:contributor.committeemember

• Guo, Xulin
• Soteros, Chris
• Bickis, Mikelis

• atmospheric ozone depletion
• Bayesian inference
• bent cable regression
• chlorofluorocarbon
• longitudinal data
• spatial effects

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/10388/ETD-2012-08-636

OAI identifier oai:identifier

oai:harvest.usask.ca:10388/ETD-2012-08-636