Regional mixed-effects height–diameter models for loblolly pine (Pinus taeda L.) plantations

European Journal of Forest Research (Impact Factor: 2.1). 04/2007; 126(2):253-262. DOI: 10.1007/s10342-006-0141-7


A height–diameter mixed-effects model was developed for loblolly pine (Pinus taeda L.) plantations in the southeastern US. Data were obtained from a region-wide thinning study established by the Loblolly
Pine Growth and Yield Research Cooperative at Virginia Tech. The height–diameter model was based on an allometric function,
which was linearized to include both fixed- and random-effects parameters. A test of regional-specific fixed-effects parameters
indicated that separate equations were needed to estimate total tree heights in the Piedmont and Coastal Plain physiographic
regions. The effect of sample size on the ability to estimate random-effects parameters in a new plot was analyzed. For both
regions, an increase in the number of sample trees decreased the bias when the equation was applied to independent data. This
investigation showed that the use of a calibrated response using one sample tree per plot makes the inclusion of additional
predictor variables (e.g., stand density) unnecessary. A numerical example demonstrates the methodology used to predict random
effects parameters, and thus, to estimate plot specific height–diameter relationships.

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Available from: Harold E. Burkhart, May 17, 2014
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    • "In a mixed-effects model, both fixed and random parameters are simultaneously estimated, which allows variability for given phenomena among various factor levels to be modeled (Lindstrom and Bates 1990). This characteristic makes mixed-effects models more efficient when prediction for a new individual is required and prior information is available (Lappi and Bailey 1988, Gregoire et al. 1995, Garber and Maguire 2003, Leites and Robinson 2004, Trincado et al. 2007). "
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    ABSTRACT: Quantification of forest biomass is important for practical forestry and for scientific purposes. It is fundamental to develop generic individual-tree biomass models suitable for large-scale forest biomass estimation. However, compatibility of forest biomass estimates at different scales may become a problem. We developed generic individual-tree biomass models using a mixed-effects modeling approach based on aboveground biomass data of Masson pine (Pinus massoniana Lamb.) from nine provinces in southern China. Mixed-effects modeling could provide an effective approach to solving the compatibility of forest biomass estimates at different scales. A simple allometric function requiring diameter at breast height was used as a base model to construct generic individual-tree mixed-effects biomass models. Two factors of tree origin (natural and planted forests) and geographic region (nine provinces or three subregions) were included as random effect factors in the models. The results showed that the mixed-effects model not only provided more accurate estimates, but also possessed good universality compared with the population average model. We, therefore, recommend the mixed-effects model 17 to estimate national and regional-scale biomass for Masson pine in southern China. The mixed-effects modeling approach is versatile and can also be applied to construct generic individual-tree models for other tree species and variables.
    Southern Forests: a Journal of Forest Science 02/2014; 76(1):47-56. DOI:10.2989/20702620.2013.870389 · 0.90 Impact Factor
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    • "To account for growing condition differences among stands for the same species, in addition to D, these models contain measures of site quality and/or stand density, among others. Studies have shown that a calibrated mixedeffects H–D model often produces better predictions than a region-wide H–D model containing stand-level regressors (Trincado et al. 2007, Temesgen et al. 2008, Huang et al. 2009). Mixed-effects models fit using plot-level data can also be calibrated at the plot level during operational inventories, providing more localised H–D relationships within a stand. "
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    ABSTRACT: To demonstrate the utility of mixed-effects height–diameter models when conducting forest inventories, mixed-effects height–diameter models are presented for several commercially and ecologically important conifers in the inland Northwest of the USA. After obtaining height–diameter measurements from a plot/stand of interest, these mixed-effects models can be calibrated to produce localised individual tree height estimates. An example of model calibration is provided. Based on model calibration results using independent data, the use of three to five trees for a particular species from a plot to calibrate the model will likely provide a reasonable compromise between predictive ability and field sampling times. If calibrated at the stand level, three trees could be used but larger sample sizes of 10 or 15 for an individual species may be reasonable. Similar mixed-effects height–diameter models could also be developed for species in the Southern Hemisphere.
    Southern Forests: a Journal of Forest Science 02/2014; 76(1):1-9. DOI:10.2989/20702620.2013.870396 · 0.90 Impact Factor
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    • "The height-diameter relationship differs from one stand to another due to differences in site quality, stand age, and silvicultural treatments, and even within the same stand due to differing competitive situation among the trees (e.g., Calama and Montero 2004; Sharma and Parton 2007; Trincado et al. 2007; Schmidt et al. 2011). "
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    ABSTRACT: We developed nonlinear mixed effects height-diameter models for three major tree species: Norway spruce (Picea abies [L.] Karst.); Scots pine (Pinus sylvestris L.); and downy birch (Betula pubescens [Ehrh.]) in Norway. We used data from four Norwegian national forest inventory (NFI) cycles (7th–10th NFI cycle) as model fitting data and data from the 6th NFI cycle as validation data. Among several bi-parametric functions tested as base functions in a preliminary analysis, the Näslund function showed the smallest residual variations, and therefore it was extended by incorporating stand variables as covariates that act as modifiers of the original parameters of the Näslund function. Sample plot-level random effects were also included in order to account for inter-plot variations within the populations. Unlike a basic mixed effects model, the extended mixed model described larger parts of variations in the height-diameter relationships and predicted heights without significant bias for validation data from the sample plots, where all measured heights of the focused species (species used for species-specific model) were used to predict random effects. For species independent models, when measured heights of other than focused species were used to predict random effects, a significant height prediction bias occurred. This bias could be reduced for certain diameter ranges by applying an extended ordinary least square model. We recommend using extended mixed effects models to estimate the missing heights on NFI sample plots and other sample plots, where measured tree heights of the focused species are available for prediction of random effects. When measured heights are not available, the extended ordinary least square model can be used.
    Forest Science and Technology 01/2014; DOI:10.1080/21580103.2014.957354
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