Modeling Aspen Tree Mortality Using Modified GEE Approach for Irregular Time Intervals

• Activity Number: 478
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Suborna Shekhor Ahmed*+ and Valerie LeMay and Changhui Peng and Zhihai Ma
• Companies: University of British Columbia and University of British Columbia and University of Quebec at Montreal and University of Quebec at Montreal
• Keywords: irregular time intervals ; modified GEE ; maximum likelihood estimator ; modified logistic regression ; survival analysis ; autocorrelation

Abstract

A probability of survival model was used to predict regular mortality of the aspen (Populus tremuloides Michx) tree species in Alberta, Canada. For tree survival, commonly permanent sample plot (PSP) data with repeated measures of individual trees at irregular time intervals are used. As a result, the logistic model was modified for survival under irregular time intervals (Modified Logistic Model). Also, autocorrelation within trees under irregular time intervals was addressed by developing a modified Generalized Estimating Equations (GEE) approach. In the Modified GEE approach, the error correlation structure was adjusted using the tree-specific time intervals. The Maximum Likelihood estimator for the Modified Logistic Model assuming no autocorrelation was used to obtain the initial estimate of the vector of model parameters. Then, the Modified Logistic Model was fit using the modified GEE approach to obtain final estimates. Monte Carlo simulations indicate that the resulting estimators are approximately unbiased and are reasonably precise.