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A Multivariate Simultaneous Prediction System for Stand Growth and Yield with Fixed and Random Effects

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Forest biometricians often deal with a simultaneously interdependent model system in which common stand characteristics such as dominant height, basal area, and total volume are included. Permanent plots with some specific design are usually the main source of data for such a model system to evaluate stand growth and yield in conjunction with different silvicultural treatments or site conditions. Two basic sources of errors are very common for such data. One is within-plot error, and the other is the variation from plot to plot. Within-plot variation is usually modeled by a reasonable variance function that accounts for within-plot heteroscedasticity and correlation. The between-plot variation can be modeled by random effects that allow parameters in the model to be varied from plot to plot. The more information available on these sources of variation, the more precise the predictions of the stand characteristics for a new observation. The interdependency among the components in the system is another key to the precision of the prediction. The observed components in the system can be used to improve the prediction of the unobserved components by accounting for the contemporaneous correlation among the components. A simultaneous system containing components of a nonlinear mixed effects dominant height growth model, a log-linear basal area model, and a log-linear total volume model is developed for slash pine (Pinus elliottii Engelm.) plantations with different silvicultural treatments. Accounting for both contemporaneous correlation and random effects, we have shown the gains in the precision of the prediction of new observations that were obtained from the recommended simultaneous model system, with detailed examples for distinct situations. It has been demonstrated that dominant height is the fundamental component in the three-component system. With contemporaneous correlation and random effects for dominant height considered, including random effects in basal area and total volume model proved to be unnecessary. Between-plot variation is the main source of error for dominant height prediction, dominant height itself dominates the precision of basal area prediction, and basal area itself is the main source of error for total volume prediction. With both random effects in dominant height and contemporaneous correlations among the three components considered, the error bound (half the 95% confidence interval divided by the predicted value) of total volume prediction decreased from 52.6% to 5.8%. For. Sci. 47(4):550–562.
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Keywords: Linear and nonlinear mixed effects model; confidence intervals of predictions; environmental management; forest; forest management; forest resources; forestry; forestry research; forestry science; intensive forest management; natural resource management; natural resources; seemingly unrelated regression

Document Type: Miscellaneous

Affiliations: 1: Assistant Research Scientist Department of Psychiatry, University of New York School of Medicine, 550 First Ave., New York, NY, 10016, Phone: (212) 263-7863; Fax: (212) 263-6457 2: Professor D.B. Warnell School of Forest Resources, The University of Georgia, Athens, Georgia, 30605, 3: Professor D.B. Warnell School of Forest Resources, The University of Georgia, Athens, Georgia, 30605,

Publication date: 2001-11-01

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.

    2016 Impact Factor: 1.782 (Rank 17/64 in forestry)

    Average time from submission to first decision: 62.5 days*
    June 1, 2016 to Feb. 28, 2017

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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