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Journal of Applied Mathematics
Volume 2014, Article ID 783494, 8 pages
http://dx.doi.org/10.1155/2014/783494
Research Article

Bayesian Analysis for Dynamic Generalized Linear Latent Model with Application to Tree Survival Rate

1School of Mathematics & Computation Sciences, Anqing Normal University, Anqing 246011, China
2Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China

Received 8 January 2014; Revised 10 June 2014; Accepted 18 June 2014; Published 7 July 2014

Academic Editor: Jen-Tzung Chien

Copyright © 2014 Yu-sheng Cheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Logistic regression model is the most popular regression technique, available for modeling categorical data especially for dichotomous variables. Classic logistic regression model is typically used to interpret relationship between response variables and explanatory variables. However, in real applications, most data sets are collected in follow-up, which leads to the temporal correlation among the data. In order to characterize the different variables correlations, a new method about the latent variables is introduced in this study. At the same time, the latent variables about AR (1) model are used to depict time dependence. In the framework of Bayesian analysis, parameters estimates and statistical inferences are carried out via Gibbs sampler with Metropolis-Hastings (MH) algorithm. Model comparison, based on the Bayes factor, and forecasting/smoothing of the survival rate of the tree are established. A simulation study is conducted to assess the performance of the proposed method and a pika data set is analyzed to illustrate the real application. Since Bayes factor approaches vary significantly, efficiency tests have been performed in order to decide which solution provides a better tool for the analysis of real relational data sets.