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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Chain binomial models and binomial autoregressive processes.

Christian H Weiss1, Philip K Pollett

  • 1Department of Mathematics, Darmstadt University of Technology, Schlossgartenstrasse 7, 64289 Darmstadt, Germany. weiss@mathematik.tu-darmstadt.de

Biometrics
|December 14, 2011
PubMed
Summary
This summary is machine-generated.

This study links chain-binomial models in ecology and epidemiology to binomial autoregressive (AR) processes. New findings provide insights into lag-conditional distributions and parameter estimation for these ecological and epidemiological models.

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Last Updated: May 26, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

  • Ecology
  • Epidemiology
  • Statistical Modeling

Background:

  • Chain-binomial models are widely used in ecology and epidemiology.
  • Understanding the statistical properties of these models is crucial for accurate data analysis.

Purpose of the Study:

  • To establish a connection between chain-binomial models and binomial autoregressive (AR) processes.
  • To derive new results for binomial AR processes, including lag-conditional distributions.
  • To explore parameter estimation methods for ecological and epidemiological models.

Main Methods:

  • Establishing a theoretical link between chain-binomial models and binomial AR processes.
  • Deriving analytical expressions for lag-conditional distributions.
  • Developing and evaluating two parameter estimation approaches.
  • Analyzing asymptotic distributions and finite-sample performance of estimators.

Main Results:

  • A novel connection is established between chain-binomial models and binomial AR processes.
  • New expressions for lag-conditional distributions and related quantities for binomial AR processes are derived.
  • Two parameter estimation methods are presented for extinction-colonization and colonization-extinction models.
  • The study includes an application to real-world ecological data.

Conclusions:

  • The established connection provides a new framework for analyzing chain-binomial models.
  • The derived results enhance the understanding of binomial AR processes.
  • The proposed estimation methods offer practical tools for ecological and epidemiological research.