Model Checking for Longitudinal Data: Root Mass Study

Date
2015-08
Authors
Zhao, Junbo
Journal Title
Journal ISSN
Volume Title
Publisher
Faculty of Graduate Studies and Research, University of Regina
Abstract

A three-year completely randomized design experiment was implemented in Alberta, Manitoba, and Saskatchewan in 2007. It was conducted by the Department of Biology, University of Regina, to measure root mass expressed per soil volume (g root /m3). Root mass data depends on four main factors: temperature, precipitation, clipping, and depth. Temperature and precipitation show climate impact. Clipping indicates Human activities impact. Depth factor could be considered to be time level (t) so that we can consider root mass data as longitudinal data. My research interests are to find a reasonable model and some significant interaction terms among the main factors. I have used the generalized estimating equation (GEE) to analyze root mass data, since GEE is an extension of the generalized linear model (GLM) for correlated data. Unlike the GLM, which is based on the maximum likelihood theory for independent observations, the GEE is based on the quasi-likelihood theory, and no assumption is made about the distribution of response observations. After applying the GEE model, I used several methods to check the model including Q-Q plot of a 2  -distribution, Wald test comparison, marginal R square, and QICu. Also, I have calculated quasi-likelihood under the independence model criterion (QIC) and Rotnizkey-Jewell’s criterion (RJC) to select a reasonable working correlation that would be the best for the GEE model. The results of this study indicated that a correlation exists between the residuals for the root mass data group by depth, which indicated the exchangeable working correlation was the best. The climate factor, i.e., temperature, was not significant in the GEE model. Two interaction terms, namely depth interaction with site and depth interaction with precipitation, were significant at α=0.05 in this model. After carrying out a model diagnostic, clusters 34 and 128 were indicated as influence points that should be removed. Finally, after removing large influence clusters, the correlations between the residuals became stronger.

Description
A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. ix, 81 p.
Keywords
Citation
Collections