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Multilevel Nonlinear Mixed-Effects Models for the Modeling of Earlywood and Latewood Microfibril Angle

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Earlywood and latewood microfibril angle (MFA) was determined at 1-millimeter intervals from disks at 1.4 meters, then at 3-meter intervals to a height of 13.7 meters, from 18 loblolly pine (Pinus taeda L.) trees grown in southeastern Texas. A modified three-parameter logistic function with mixed effects is used for modeling earlywood and latewood MFA. By making the parameters of the logistic function linear functions of height, a three-dimensional model was developed that describes the changes of earlywood and latewood MFA within the tree. A first-order autoregressive correlation structure and a variance model corresponding to a variance covariate given by the fitted values for each wood type, but in which the proportionality constant differs according to the level of wood type, was identified as the within-group correlation and variance structures. Cross-validation was used to determine model accuracy and precision. The methods of model development including determination of the height structure, which parameters should be considered random or fixed, determination of an appropriate variance-covariance structure, and prediction are addressed. Model performance was evaluated utilizing informative statistics including likelihood ratio tests (LRTs), Akaike information criterion (AIC), and Bayesian information criterion (BIC). FOR. SCI. 51(4):357–371.

Keywords: Microfibril angle; environmental management; forest; forest management; forest resources; forestry; forestry research; forestry science; loblolly pine; mixed effects models; natural resource management; natural resources; nonlinear models; repeated measurements

Document Type: Regular Article

Affiliations: 1: Research Coordinator Warnell School of Forest Resources The University of Georgia Athens GA 30602-2152 Phone: (706) 542-9724;, Fax: (706) 542-0119, Email: 2: Professor Warnell School of Forest Resources The University of Georgia Athens GA 30602-2152 Phone: (706) 542-7268, Email: 3: Wood Scientist Southern Research Station USDA Forest Service Athens GA 30602 Phone: (706) 559-4323, Email: 4: Graduate Research Assistant Warnell School of Forest Resources The University of Georgia Athens GA 30602-2152 Phone: (706) 542-9724, Email:

Publication date: August 1, 2005

More about this publication?
  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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