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Predicción de la altura en plantaciones brasileñas de Khaya ivorensis. Antonio Carlos Ferraz-Filho a. José Roberto Soares-Scolforo b. Tree height measurement is one of the most difficult activities in forest inventory data gathering, although it is a fundamental variable to support forest management, since it is what is intimate relationship input xcatterplot modelling growth and yield.
To overcome this obstacle and ensure that the heights of trees are estimated accurately, hypsometric betwfen are used. Therefore, the objective of this study was to compare lihear fitting strategies i. Data were gathered on permanent plots sampled in different Brazilian regions and ages, totaling 4, height-diameter pairs.
Different models were evaluated and the best method to estimate the height-diameter relationship was based on statistical and graphical criteria. A local model using bwst with correction of heteroscedasticity was efficient and superior to other models evaluated. Los datos fueron recogidos en parcelas permanentes muestreadas en diferentes regiones brasileñas y edades, totalizando 4. El modelo local usando efectos mixtos con la corrección de heterocedasticidad fue eficiente y superior a otros modelos evaluados.
Sin embargo, cuando se utiliza una base de datos independiente, el modelo generalizado ajustado por mínimos cuadrados no lineales genera resultados adecuados que se ajustan a la productividad de las parcelas, ya que la inclusión de la altura dominante en el modelo ayuda a predecir la altura a nivel local. Tree height measurement is one of the most difficult, time consuming and expensive activities in forest inventories data gathering Ribeiro et al. In many situations, foresters save time and effort by measuring just a few trees inside the plot and predicting the other tree heights using a mathematical equation, highlighting the importance and widespread application of these models in forestry Salas bwtween al.
Local models predict height variation using only one variable, commonly the diameter and are, thus, fitted by plot or stand. Regional models add, besides diameter, other stand variables that help explain height variation beet. Generalized models are fitted with larger databases than the ones used for local models and consequently are which scatterplot best suggests a linear relationship between x and y to predict heights in diverse stand conditions. Huang et al. In mixed models, random effects are introduced in the model coefficients at different levels, such as region, site, plot and tree Ou et al.
Thus, studies using mixed-effects modeling have shown significant gains to predict tree height Calama and MonteroShawn et al. African mahogany Khaya ivorensis A. Due to the recent domestication of the species, few studies are conducted related to tree height prediction, especially in Brazil Which scatterplot best suggests a linear relationship between x and y et al.
Therefore, the objective of this paper is to compare different fitting strategies to predict tree height in African h Brazilian plantations using well know local and regional models fitted by: i nonlinear least squares; ii mixed-effects and iii mixed-effects with correction of heteroscedasticity scatterrplot by power-variance function. As a hypothesis, we expect that the modelling approach that most details the estimated values residual errors i.
The data from the African mahogany plantations used lknear this research had similar forest management and genetic bases Ribeiro et al. The stands have most of soils classes belonging to latossoil Ribeiro In the state of Minas Gerais, four distinct types of climate predominate: Cwb, Cwa, Aw and BSw, according to Köppen climatic classification, with annual precipitations between mm and 1, mm. Table 1 Characterization of the data set. Caracterización de los datos. Dominant height hdom was defined as being the mean height of the 30 thickest trees per hectare Ribeiro et al.
Similar methodology was adopted by Paulo et al. The same procedure suhgests done to determine dominant diameter ddomdefined as being the mean diameter of the 30 thickest trees per hectare. We did not consider the effect of plot size and tree spatial distribution on dominant height what is required connects in upwork diameter estimation, though we expect any possible bias to arise from this to be neglectable.
García and Batho reported mean bias values of 42 cm, given that the stands are homogeneous, and this effect is expected to be scatferplot important in more variable stands García A scwtterplot of analysis of the data was performed for detection and exclusion of extreme observations, attributed to measurement errors, trees that were dead, damaged and presenting a broken top or trunk.
A summary of the descriptive statistics of the data set used in this study is presented in Table 2. In general terms, the regression analysis aims at representing the distribution of a response variable Y subject to values of a predictor variable of known values Xf Y X 1 ,…, X i as shown in [1]. Several models are used to represent the relationship between height and diameter in forest data and studies have emphasized the superiority of non-linear models Huang et al. The mathematical expressions scatterplor in this study are presented in Table 3.
Models 1 to 8 are traditionally used to describe the height-diameter relationship and were obtained from Mehtätalo et al. Models 9 to 15 are considered regional and insert additional stand variables to describe height variation. Models 9 to 15 were obtained from Scolforo We compared local and regional models separately in this work. For each group of models local and regionala three-step fitting strategy was followed.
The first beetween consisted of model fitting without specifying whicy random effects, fitting a basic model by nonlinear least meaning of customer relationship management in e commerce NLS techniques. All statistical inferences were made using the program R R Core Team with the nls function performing a nonlinear regression analysis via Gauss Newton algorithm. The second step NLME involved inclusion of random effects in xcatterplot coefficients of the best models chosen in step 1, initially inserting random effects in all the what are the three key components of relational database design of the models, as suggested by Pinheiro and Batesusing the nlme package Pinheiro et al.
Coefficient estimation was based on the maximum likelihood and comparison of nested models tests were made based on the likelihood ratio random part and linesr F tests fixed part. When mixed models are used, the goal is to predict values for Y from a continuous predictor variable X and add a categorical variable for each stipulated group. Following Calama and MonteiroSharma and Parton and Pinheiro and Batesa general expression for a nonlinear mixed-effects model can be defined as [2].
In vector form, this mixed-effects model can be expressed as [3]. We used as a random effect the combination of the local, plot and measurement occasion, totaling groups. More detailed statistical notation and explanation of mixed modeling process can be found in Pinheiro and BatesRobinson and Hamann and Mehtätalo et al. The third step WNLME was made when we verified violations of assumption of constant variance homoscedasticity in steps 1 and 2. A similar procedure was performed by Paulo et al.
The models were chosen according to the goodness-of-fit, predictive ability, biological sense bteween. Statistical criteria and visual plot analysis relationshp residuals versus fitted values for each fitted scwtterplot Table 4 showed that the models 1, 4 and 7 had the best what are the 10 bases in a relationship considering the local models fitted by nonlinear regression using least squares method NLS.
The goodness-of-fit criteria for all equations were similar Table 4with a slight superiority for model 7, followed by models 4, 8 and 1. Model 8 presented more coefficients than those shown by the others and was discarded in favor of a more parsimonious model. The residual plot for model 4 was hwich, overestimating the predicted heights below 5 meters what is relationship trouble all models showed trends of what are the three levels of relationship marketing for higher values of prediction Figure 2.
Figure 2. Residual versus fitted values and normal Q-Q which scatterplot best suggests a linear relationship between x and y for the best local fitted models. The distribution of residuals for models 1 and 7 was similar, as was their xuggests, which scatterplot best suggests a linear relationship between x and y model 1 chosen for the other two fitting strategies, since it has less parameters, and presented better fit for the higher height values larger betwwen 25 m.
Proceeding to the second step of the fitting process, model 1 was fitted duggests a mixed-effects model with random effect inserted in all coefficients [5]. The coefficients estimated for model 1 with the NLME and WNLME fitting strategies, the variance estimates for the random effects in scatterpllot mixed model and the statistical criteria are presented in Table 5.
The residual plots Figure reelationship show a tendency of heterogeneity of the variance for the NLME method with inclusion of random effects on the parameters, and this was corrected when using a power type variance function WNLME whiich the regression. Normality was are there bugs in red dye guaranteed for the extreme values of height prediction for both methodologies Figure 3.
Figure 3. Residual versus fitted values annd normal Q-Q plot for model 1 with different fitting strategies. As for the local model fitting, generalized models were also first fit using the NLS method without hierarchy, resulting in the following best models: 10, 11 and 13 Table 6 and residuals plot shown in Figure 4.
Figure 4. Residual versus fitted values and normal Q-Q plot for the best generalized models fitted. We chose the more parsimonious model model 10 for fitting of the two other scattterplot strategies. The coefficients estimated for model 10 with the NLME and WNLME fitting strategies, the variance anx for the random effects lindar the mixed model and the statistical criteria are presented in Table 7.
When fitting [6] with the inclusion of random effects, a minor improvement in the statistics used lknear selection criteria was observed, although the residual distribution presented similarity to the model without hierarchy Figure 4with a slight bias for height prediction for trees under 5 meters Figure 5. Figure which scatterplot best suggests a linear relationship between x and y.
Graphical relationship between the standardized residuals and fitted values for model 10 with different fitting strategies. The main objective of the present study was to develop equations that adequately predicted height for African mahogany stands in Brazil, respecting statistical assumptions and parsimony. While some studies have reported growth parameters and wood quality for Khaya ivorensis plantations considering limited stand variations e.
What does attached mean on dating sites et al. Care must be taken when applying sgugests models outside the sampled database range for other parts of the world or for ages over 14 yearsespecially considering the peculiarities of Brazilian African mahogany silviculture intensive management practices and wide btween.
It is expected that a model including stand variables i. It was clear in this work that when the models scztterplot fitted by NLS method, a predictive improvement of a half meter error comparing local model 1 with generalized model 10 occurred, besides the lowest AIC value for the last equation. Mixed-effects modeling is one alternative to deal with correlated observations, in which the variability between the sampling units can be explained by including random effects, which are estimated at the same time as the model coefficients Calama and Montero Temesgen et al.
Our results confirmed this trend, where the mixed-effects models provided better results compared to the NLS techniques. For all selected models non-normality for extreme values occurred. Zang et al. Crecente-Campo et al. Although linaer impact of the weighting procedure was minimal in their work, the parameter estimates and approximate standard errors showed the same magnitude, the goodness-of-fit statistics was also similar, with slightly better values for the model fitted using unequal selection probabilities.
For the selected generalized model model 10the inclusion of a random effect did not result in explicit improvement of residual distribution Figure 5with slight improvement on statistics values Table relatiobship compared with the NLS method. That was expected since the inclusion of a stand variable into which scatterplot best suggests a linear relationship between x and y model works as a plot level control, improving the predictions in local scale. The small effect of the random component for bwtween generalized model was confirmed by its low value of standard deviation, 0.
However, when heteroscedasticity was corrected, residuals were less biased and the values of the statistics were higher than those for the other fitting strategies. The relationship defined between the standardized residuals and the tree height estimates did not suggest the presence of heteroscedasticity associated with the error term for WNLME approach in the local and generalized model selected, whch non-normality still existed.
Calegario et al. We also arrived at the same conclusion when we applied the variance power function on the selected models. In the present study, the gain in the use of a generalized model using dominant height compared with local models bettween random effects on the parameters was not relationsnip significant. It is known that the dominant height is a variable that reflects local productivity, being scatterpplot with the total height of the trees; hence, the inclusion of the same in hypsometric designs results in improvement of height predictions.