Graduate Thesis Or Dissertation
 

Generalized linear mixed models with censored covariates

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/794081609

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  • This dissertation is about statistical methods for data analysis using generalized linear mixed models (GLMMs) with censored covariates. Special attention in given to the particular problem of inference about age-specific reproductive success in wild animal populations using some animals with known ages and some animals with ages only known to exceed some lower bound. GLMMs allow for non-normal response distributions, such as a Poisson distribution for the number of offspring from a parent in one year, and they account for the correlation of repeated responses from the same observational unit, such as the correlation of the number of offspring from the same parent over multiple years. A computational algorithm for maximum likelihood estimation and two approximate estimation methods are proposed. The full solution uses the EM algorithm with Markov Chain Monte Carlo techniques for the E-step. The approximations are presented as techniques that may be nearly as good as the full maximum likelihood analysis but that are easier for wildlife biologists to use. One uses a Laplace approximation to the log-likelihood to capitalize on existing programs for GLMM estimation. The other is a regression calibration method in which the missing ages are simply replaced by predicted values. The full likelihood analysis is demonstrated on a study of age-specific reproductive success of Northern Spotted Owls (Strix occidentalis caurina). A simulation study was used to evaluate the operating characteristics of the three methods and to highlight the potential gains of these methods over the common practice of ignoring animals with unknown ages. The conditions of the simulations were chosen to roughly match those in the spotted owl study. It appears that the use of the owls with censored ages reduces the widths of 95% confidence intervals for important regression coefficients by about 39% if full maximum likelihood analysis is used. The corresponding reduction for the regression calibration estimator is about 27%. A main conclusion of this thesis is that the regression calibration estimator can offer substantially higher efficiency than the commonly used GLMM estimator with animals of unknown ages excluded and, importantly, wildlife biologists can use it with computing modules that are already available in standard statistical computing packages.
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file details Giovanini_PhD_Dissertation.pdf 2017-08-19 Öffentlich Herunterladen