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

By Zixing Fang, R. Bailey, B. Shiver. Forestry sciences, 2001

50 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Environmental Engineering, Nature and Landscape Conservation

View Paper: https://www.semanticscholar.org/paper/858ade2a50d680aa08ce65edce91ccceda0e77b2

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Citations in the corpus

Forest Growth and Yield Modeling (2011, methodology): “Lynch, 2001) or maximum likelihood (e.g. Fang et al., 2001; Cao and Strub, 2008) methods are appropriate.”
Modelling and prediction of dominant height and site index of Eucalyptus globulus plantations using a nonlinear mixed-effects model approach (2007, unknown): “However, as noted by Gregoire et al. (1995), the errors resulting from fitting models using PSP data are often serially correlated within plots as they are repeatedly measured, heteroscedastic among plots, and, possibly, also heteroscedastic among remeasurements within plots.”
Height-diameter models with random coefficients and site variables for tree species of Central Maine (2008, background): “These allometric relationships also change with silvicultural practices, such as thinning, that alter competitive relationships among neighboring trees [9, 13].”
Dominant height growth equations including site attributes in the generalized algebraic difference approach (2008, unknown): “modelling local variability (Lappi and Bailey 1988; Fang et al. 2001; Calama and Montero 2004).”
Interregional nonlinear height-diameter model with random coefficients for stone pine in Spain (2004, methodology): “…parameters into the model allows us to consider two different situations in a predictive role (Vonesh and Chinchilli 1997; Fang and Bailey 2001; Fang et al. 2001): (1) Fixed-effects response pattern: prediction of tree height in those stands where diameter and stand variables included in the…”
Cone and seed production from stone pine (Pinus pinea L.) stands in Central Range (Spain) (2006, unknown): “The use of multivariate ML mixed models in forest science is very recent (Fang et al. 2001; Hall and Clutter 2004; Zhang and Borders 2004).”
Generic biomass functions for Common beech (Fagus sylvatica) in Central Europe: predictions and components of uncertainty (2008, background): “This finding corroborates the finding of Fang et al. (2001), where the inclusion of the predictor dominant height accounted for the differences between stands, that were formerly accounted for by random effects.”