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Engelmann spruce site index models: a comparison of model functions and parameterizations.

Nigh G - PLoS ONE (2015)

Bottom Line: Engelmann spruce (Picea engelmannii Parry ex Engelm.) is a high-elevation species found in western Canada and western USA.The model parameterizations that were tested are indicator variables, mixed-effects, GADA, and g-GADA.Model parameterization had more of an influence on the fit than did model formulation, with the indicator variable method providing the best fit, followed by the mixed-effects modelling (9% increase in the variance for the Chapman-Richards and Schumacher formulations over the indicator variable parameterization), g-GADA (optimal approach) (335% increase in the variance), and the GADA/g-GADA (with the GADA parameterization) (346% increase in the variance).

View Article: PubMed Central - PubMed

Affiliation: Forest Analysis and Inventory Branch, British Columbia Ministry of Forests, Lands and Natural Resource Operations, Victoria, British Columbia, Canada.

ABSTRACT
Engelmann spruce (Picea engelmannii Parry ex Engelm.) is a high-elevation species found in western Canada and western USA. As this species becomes increasingly targeted for harvesting, better height growth information is required for good management of this species. This project was initiated to fill this need. The objective of the project was threefold: develop a site index model for Engelmann spruce; compare the fits and modelling and application issues between three model formulations and four parameterizations; and more closely examine the grounded-Generalized Algebraic Difference Approach (g-GADA) model parameterization. The model fitting data consisted of 84 stem analyzed Engelmann spruce site trees sampled across the Engelmann Spruce - Subalpine Fir biogeoclimatic zone. The fitted models were based on the Chapman-Richards function, a modified Hossfeld IV function, and the Schumacher function. The model parameterizations that were tested are indicator variables, mixed-effects, GADA, and g-GADA. Model evaluation was based on the finite-sample corrected version of Akaike's Information Criteria and the estimated variance. Model parameterization had more of an influence on the fit than did model formulation, with the indicator variable method providing the best fit, followed by the mixed-effects modelling (9% increase in the variance for the Chapman-Richards and Schumacher formulations over the indicator variable parameterization), g-GADA (optimal approach) (335% increase in the variance), and the GADA/g-GADA (with the GADA parameterization) (346% increase in the variance). Factors related to the application of the model must be considered when selecting the model for use as the best fitting methods have the most barriers in their application in terms of data and software requirements.

No MeSH data available.


Related in: MedlinePlus

Height-breast height age trajectories for the Engelmann spruce data.
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pone.0124079.g002: Height-breast height age trajectories for the Engelmann spruce data.

Mentions: The indicator variable parameterization is the most flexible since there are no restrictions on the values that the parameters can take. Therefore, this parameterization results in models with the best fit, thus providing a benchmark among the models being compared. The superior fit of this parameterization (and the mixed-effects parameterization) could also be partially due to having more parameters than the GADA parameterizations. The main disadvantage with this parameterization is that in order to calibrate the fitted models, at least two height-age pairs of data (one pair for each parameter that needs to be estimated) are required. In general, if it were the case that all parameters were local, the outcome of the model fitting step would be to just determine the best functional form of the model; without any global parameters all of the parameters would have to be determined in the calibration step. The other disadvantage with this parameterization is that some parameter estimates may not be biologically feasible. This was the case for the asymptote parameters for the HIV and SCH models. Many of the sample trees exhibited nearly linear growth patterns at older ages (Fig 2). The slowing in height growth at older ages that is typical for most species helps define the asymptote. The asymptote parameter for the trees that do not show strong asymptotic growth is poorly estimated. Despite its drawbacks, this parameterization is useful because it helps identify global and local parameters. As well, the parameter estimates can lead to potential parameterizations for the GADA and g-GADA methods.


Engelmann spruce site index models: a comparison of model functions and parameterizations.

Nigh G - PLoS ONE (2015)

Height-breast height age trajectories for the Engelmann spruce data.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4390286&req=5

pone.0124079.g002: Height-breast height age trajectories for the Engelmann spruce data.
Mentions: The indicator variable parameterization is the most flexible since there are no restrictions on the values that the parameters can take. Therefore, this parameterization results in models with the best fit, thus providing a benchmark among the models being compared. The superior fit of this parameterization (and the mixed-effects parameterization) could also be partially due to having more parameters than the GADA parameterizations. The main disadvantage with this parameterization is that in order to calibrate the fitted models, at least two height-age pairs of data (one pair for each parameter that needs to be estimated) are required. In general, if it were the case that all parameters were local, the outcome of the model fitting step would be to just determine the best functional form of the model; without any global parameters all of the parameters would have to be determined in the calibration step. The other disadvantage with this parameterization is that some parameter estimates may not be biologically feasible. This was the case for the asymptote parameters for the HIV and SCH models. Many of the sample trees exhibited nearly linear growth patterns at older ages (Fig 2). The slowing in height growth at older ages that is typical for most species helps define the asymptote. The asymptote parameter for the trees that do not show strong asymptotic growth is poorly estimated. Despite its drawbacks, this parameterization is useful because it helps identify global and local parameters. As well, the parameter estimates can lead to potential parameterizations for the GADA and g-GADA methods.

Bottom Line: Engelmann spruce (Picea engelmannii Parry ex Engelm.) is a high-elevation species found in western Canada and western USA.The model parameterizations that were tested are indicator variables, mixed-effects, GADA, and g-GADA.Model parameterization had more of an influence on the fit than did model formulation, with the indicator variable method providing the best fit, followed by the mixed-effects modelling (9% increase in the variance for the Chapman-Richards and Schumacher formulations over the indicator variable parameterization), g-GADA (optimal approach) (335% increase in the variance), and the GADA/g-GADA (with the GADA parameterization) (346% increase in the variance).

View Article: PubMed Central - PubMed

Affiliation: Forest Analysis and Inventory Branch, British Columbia Ministry of Forests, Lands and Natural Resource Operations, Victoria, British Columbia, Canada.

ABSTRACT
Engelmann spruce (Picea engelmannii Parry ex Engelm.) is a high-elevation species found in western Canada and western USA. As this species becomes increasingly targeted for harvesting, better height growth information is required for good management of this species. This project was initiated to fill this need. The objective of the project was threefold: develop a site index model for Engelmann spruce; compare the fits and modelling and application issues between three model formulations and four parameterizations; and more closely examine the grounded-Generalized Algebraic Difference Approach (g-GADA) model parameterization. The model fitting data consisted of 84 stem analyzed Engelmann spruce site trees sampled across the Engelmann Spruce - Subalpine Fir biogeoclimatic zone. The fitted models were based on the Chapman-Richards function, a modified Hossfeld IV function, and the Schumacher function. The model parameterizations that were tested are indicator variables, mixed-effects, GADA, and g-GADA. Model evaluation was based on the finite-sample corrected version of Akaike's Information Criteria and the estimated variance. Model parameterization had more of an influence on the fit than did model formulation, with the indicator variable method providing the best fit, followed by the mixed-effects modelling (9% increase in the variance for the Chapman-Richards and Schumacher formulations over the indicator variable parameterization), g-GADA (optimal approach) (335% increase in the variance), and the GADA/g-GADA (with the GADA parameterization) (346% increase in the variance). Factors related to the application of the model must be considered when selecting the model for use as the best fitting methods have the most barriers in their application in terms of data and software requirements.

No MeSH data available.


Related in: MedlinePlus