A Multilevel Approach to Individual Tree Survival Prediction

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Abstract:

Traditionally, modeling of permanent plot individual tree survival has not considered the multiple sources of heterogeneity and correlation that may arise due to the multilevel data structure inherent in the design (e.g., clustering of trees within a plot). Permanent plots are sampled periodically; therefore, data are interval-censored because it is only known that a tree died between two successive measurement occasions. Here, we adopt the complementary log–log (CLL) function for modeling permanent plot interval-censored individual tree survival data. The CLL function is derived directly from the likelihood function of a fully specified statistical model that accounts for interval censoring. In addition, our CLL model considers silvicultural treatment effects on survival. Our data are from young permanent plot loblolly pine plantations that have been measured annually beginning at age 1 year. Each plot was randomly assigned one of four cultural treatments:control (C), herbicide (H), fertilization (F), and herbicide and fertilization (HF). Here we extend the individual tree survival CLL model to allow for trees within a plot and plot level random effects. We demonstrate individual tree survival predictions with and without the inclusion of random effects.

Keywords: Hazard function; complementary log-log function; interval-censored; proportional hazards; random effects

Document Type: Research Article

Affiliations: 1: Charles E. Rose Jr., Mathematical Statistician, Anthrax Vaccine Safety Team NIP/CDC, 1600 Clifton Rd., Mailstop E-61, Atlanta, GA 30333—Phone: (404) 639-3028;, Fax: (404) 639-2483, Email: cvr7@cdc.gov. 2: Daniel B. Hall, Associate Professor, University of Georgia, Department of Statistics, Athens, GA 30602-1952—Phone: (706) 542-3302;, Email: dhall@stat.uga.edu. 3: Barry D. Shiver, Professor, University of Georgia, Daniel B. Warnell School of Forest Resources, Athens, GA 30602—Phone: (706) 542-3009;, Email: shiver@smokey.forestry.uga.edu. 4: Michael L. Clutter, Professor, University of Georgia, Daniel B. Warnell School of Forest Resources, Athens, GA 30602—Phone:(706) 542-5448;, Email: mclutter@smokey.forestry.uga.edu. 5: Bruce Borders, Professor, University of Georgia, Daniel B. Warnell School of Forest Resources, Athens, GA 30602—Phone: (706) 542-6205;, Email: bborders@arches.uga.edu.

Publication date: January 1, 2006

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