scholarly journals A Bayesian Approach to Estimating Seemingly Unrelated Regression for Tree Biomass Model Systems

Forests ◽  
2020 ◽  
Vol 11 (12) ◽  
pp. 1302
Author(s):  
Longfei Xie ◽  
Fengri Li ◽  
Lianjun Zhang ◽  
Faris Rafi Almay Widagdo ◽  
Lihu Dong
Keyword(s):  
Bayesian Approach ◽  
Bayesian Methods ◽  
Model Fitting ◽  
Seemingly Unrelated Regression ◽  
Model Systems ◽  
Informative Priors ◽  
Tree Biomass ◽  
Tree Diameter ◽  
Biomass Models ◽  
Unrelated Regression

Accurate estimation of tree biomass is required for accounting for and monitoring forest carbon stocking. Allometric biomass equations constructed by classical statistical methods are widely used to predict tree biomass in forest ecosystems. In this study, a Bayesian approach was proposed and applied to develop two additive biomass model systems: one with tree diameter at breast height as the only predictor and the other with both tree diameter and total height as the predictors for planted Korean larch (Larix olgensis Henry) in the Northeast, P.R. China. The seemingly unrelated regression (SUR) was used to fit the simultaneous equations of four tree components (i.e., stem, branch, foliage, and root). The model parameters were estimated by feasible generalized least squares (FGLS) and Bayesian methods using either non-informative priors or informative priors. The results showed that adding tree height to the model systems improved the model fitting and performance for the stem, branch, and foliage biomass models, but much less for the root biomass models. The Bayesian methods on the SUR models produced narrower 95% prediction intervals than did the classical FGLS method, indicating higher computing efficiency and more stable model predictions, especially for small sample sizes. Furthermore, the Bayesian methods with informative priors performed better (smaller values of deviance information criterion (DIC)) than those with the non-informative priors. Therefore, our results demonstrated the advantages of applying the Bayesian methods on the SUR biomass models, not only obtaining better model fitting and predictions, but also offering the assessment and evaluation of the uncertainties for constructing and updating tree biomass models.

Simultaneous estimation of biomass models for 13 tree species: effects of compatible additivity requirements

2017 ◽  
Vol 47 (6) ◽  
pp. 765-776 ◽  
Author(s):  
Thomas Nord-Larsen ◽  
Henrik Meilby ◽  
Jens Peter Skovsgaard
Keyword(s):  
Ordinary Least Squares ◽  
Seemingly Unrelated Regression ◽  
Model Systems ◽  
Simultaneous Estimation ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Biomass Models ◽  
Unrelated Regression ◽  
Biomass Components ◽  
Species Specific

A desirable feature of biomass models distinguishing different tree components is compatible additivity of the component functions. Due to forcing of parameter estimates, such additivity is achieved at an expense of precision of the component functions. This study aimed to analyse the loss of precision incurred by forcing of parameters in tree biomass models due to (i) additivity constraints, (ii) combining global and species-specific parameters, and (iii) estimating component functions simultaneously as a system instead of as individual equations. Based on biomass data from 697 trees including 13 different species, we estimated a set of compatibly additive, nonlinear biomass models using simultaneous estimation and compared these with less restricted model systems. In line with other similar studies, the overall model system explained 88%–99% of the variation in individual biomass components. Compared with the unrestricted model, restricting parameters to obtain compatible additivity resulted in a change in RMSE of –0.6% to 5.4%. When restricting parameter estimates using both species-specific and global parameters, RMSE increased by 1.7%–13.1%. Estimating model parameters using simultaneous estimation (nonlinear iterated seemingly unrelated regression, NSUR) increased model bias compared with ordinary least squares estimation (OLS) for most biomass components. Contrary to expectations, NSUR estimation did not lead to a reduction in the standard error of estimates.

scholarly journals Bayesian Skew Normal Seemingly Unrelated Regression Modelling of Gross Regional Domestic Product

2018 ◽  
pp. 869-879
Author(s):  
Agus Budi Santosa ◽  
Nur Iriawan ◽  
Setiawan Setiawan ◽  
Mohammad Dokhi
Keyword(s):  
Bayesian Approach ◽  
Absolute Error ◽  
Seemingly Unrelated Regression ◽  
Percentage Error ◽  
Actuarial Science ◽  
Normal Distributions ◽  
Unrelated Regression ◽  
Normal Error ◽  
Skew Distribution ◽  
Skew Normal

The assumption of the error normality in the regression model was often questioned especially in cases where there was an outlier, which causes the behavior of asymmetric data. To overcome this, without data transformation, we could use skew distribution. This distribution was very important and applicable in various fields of science such as finance, economics, actuarial science, medicine, biology, investment. Skew Normal distributions had been proven to have a convenient for calculating bias in data with asymmetric behavior. This study aims to model SUR with Skew Normal error using Bayesian approach applied to East Java GRDP data. This study would compared two types of models, namely models with Normal distributed errors and models with Skew Normal distributed errors. The result of parameter estimation with Bayesian approach shows that SUR Skew Normal model was more suitable for East Java GRDP modeling rather than using normal error model. This was based on their smaller Root of Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) value. 

scholarly journals Comparison of Tree Biomass Modeling Approaches for Larch (Larix olgensis Henry) Trees in Northeast China

Forests ◽  
2020 ◽  
Vol 11 (2) ◽  
pp. 202 ◽  
Author(s):  
Lihu Dong ◽  
Yue Zhang ◽  
Zhuo Zhang ◽  
Longfei Xie ◽  
Fengri Li
Keyword(s):  
Random Effects ◽  
Aboveground Biomass ◽  
Northeast China ◽  
Model Systems ◽  
Larix Olgensis ◽  
Tree Biomass ◽  
Modeling Approaches ◽  
Biomass Models ◽  
Larix Olgensis Henry ◽  
Biomass Modeling

Accurate quantification of tree biomass is critical and essential for calculating carbon storage, as well as for studying climate change, forest health, forest productivity, nutrient cycling, etc. Tree biomass is typically estimated using statistical models. Although various biomass models have been developed thus far, most of them lack a detailed investigation of the additivity properties of biomass components and inherent correlations among the components and aboveground biomass. This study compared the nonadditive and additive biomass models for larch (Larix olgensis Henry) trees in Northeast China. For the nonadditive models, the base model (BM) and mixed effects model (MEM) separately fit the aboveground and component biomass, and they ignore the inherent correlation between the aboveground and component biomass of the same tree sample. For the additive models, two aggregated model systems with one (AMS1) and no constraints (AMS2) and two disaggregated model systems without (DMS1) and with an aboveground biomass model (DMS2) were fitted simultaneously by weighted nonlinear seemingly unrelated regression (NSUR) and applied to ensure additivity properties. Following this, the six biomass modeling approaches were compared to improve the prediction accuracy of these models. The results showed that the MEM with random effects had better model fitting and performance than the BM, AMS1, AMS2, DMS1, and DMS2; however, when no subsample was available to calculate random effects, AMS1, AMS2, DMS1, and DMS2 could be recommended. There was no single biomass modeling approach to predict biomass that was best for all aboveground and component biomass except for MEM. The overall ranking of models based on the fit and validation statistics obeyed the following order: MEM > DMS1 > AMS2 > AMS1> DMS2 > BM. This article emphasized more on the methodologies and it was expected that the methods could be applied by other researchers to develop similar systems of the biomass models for other species, and to verify the differences between the aggregated and disaggregated model systems. Overall, all biomass models in this study have the benefit of being able to predict aboveground and component biomass for larch trees and to be used to predict biomass of larch plantations in Northeast China.

scholarly journals Evaluation of Stand Biomass Estimation Methods for Major Forest Types in the Eastern Da Xing’an Mountains, Northeast China

Forests ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 715
Author(s):  
Dong ◽  
Zhang ◽  
Li
Keyword(s):  
Model Fitting ◽  
Prediction Performance ◽  
Model Systems ◽  
Estimation Methods ◽  
Biomass Estimation ◽  
Forest Types ◽  
Stand Volume ◽  
Additive System ◽  
Biomass Models ◽  
Biomass Equations

Currently, forest biomass estimation methods at the regional scale have attracted the greatest attention from researchers, and the development of stand biomass models has become popular a trend. In this study, a total of 5074 measurements on 1053 permanent sample plots were obtained in the Eastern Da Xing’an Mountains, and three additive systems of stand biomass equations were developed. The first additive system (M-1) used stand variables as the predictors (i.e., stand basal area and average height), the second additive system (M-2) utilized stand volume as the sole predictor, and the third additive system (M-3) included both stand volume and biomass expansion and conversion factors (BCEFs) as the predictors. The coefficients of the three model systems were estimated with nonlinear seemingly unrelated regression (NSUR), while the heteroscedasticity of the model residuals was solved with the weight function. The jackknifing technique was used on the residuals, and several statistics were used to assess the prediction performance of each model. We comprehensively evaluated four stand biomass estimation methods (i.e., M-1, M-2, M-3 and a constant BCEF (M-4)). Here, we showed that the (1) three additive systems of stand biomass equations showed good model fitting and prediction performance, (2) M-3 significantly improved the model fitting and performance and provided the most accurate predictions for most stand biomass components, and (3) the ranking of the four stand biomass estimation methods followed the order of M-3 > M-2 > M-4 > M-1. Our results demonstrated these additive stand biomass models could be used to estimate the stand aboveground and belowground biomass for the major forest types in the Eastern Da Xing’an Mountains, although the most appropriate method depends on the available data and forest type.

scholarly journals Biomass Modelling ofAndrostachys johnsoniiPrain: A Comparison of Three Methods to Enforce Additivity

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Tarquinio Mateus Magalhães ◽  
Thomas Seifert
Keyword(s):  
Seemingly Unrelated Regression ◽  
Tree Biomass ◽  
Tree Model ◽  
Fit Statistics ◽  
Significant Bias ◽  
Parameter Restriction ◽  
Unrelated Regression ◽  
Tree Component ◽  
Component Models ◽  
Total Tree

Three methods of enforcing additivity of tree component biomass estimates into total tree biomass estimates forAndrostachys johnsoniiPrain were studied and compared, namely, the conventional (CON) method (a method that consists of using the same independent variables for all tree component models, and for total tree model, and the same weights to enforce additivity), seemingly unrelated regression (SUR) with parameter restriction, and nonlinear seemingly unrelated regression (NSUR) with parameter restriction. The CON method was found to be statistically superior to any other method of enforcing additivity, yielding excellent fit statistics and unbiased biomass estimates. The NSUR method ranked second best but was found to be biased. The SUR method was found to be the worst; it exhibited large bias and had a poor fit for the biomass. Therefore, we recommend that only the CON and NSUR methods should be used for further estimates, provided that their limitations are considered, that is, exclusion of contemporaneous correlations for the CON method and consideration of the significant bias of the NSUR method.

scholarly journals Generic Additive Allometric Models and Biomass Allocation for Two Natural Oak Species in Northeastern China

Forests ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 715
Author(s):  
Shengwang Meng ◽  
Fan Yang ◽  
Sheng Hu ◽  
Haibin Wang ◽  
Huimin Wang
Keyword(s):  
Biomass Allocation ◽  
Tree Height ◽  
Northeastern China ◽  
Seemingly Unrelated Regression ◽  
Biomass Estimation ◽  
Model Parameters ◽  
Stem Biomass ◽  
Crown Width ◽  
Biomass Models ◽  
Mongolian Oak

Current models for oak species could not accurately estimate biomass in northeastern China, since they are usually restricted to Mongolian oak (Quercus mongolica Fisch. ex Ledeb.) on local sites, and specifically, no biomass models are available for Liaodong oak (Quercuswutaishanica Mayr). The goal of this study was, therefore, to develop generic biomass models for both oak species on a large scale and evaluate the biomass allocation patterns within tree components. A total of 159 sample trees consisting of 120 Mongolian oak and 39 Liaodong oak were harvested and measured for wood (inside bark), bark, branch and foliage biomass. To account for the belowground biomass, 53 root systems were excavated following the aboveground harvest. The share of biomass allocated to different components was assessed by calculating the ratios. An aboveground additive system of biomass models and belowground equations were fitted based on predictors considering diameter (D), tree height (H), crown width (CW) and crown length (CL). Model parameters were estimated by jointly fitting the total and the components’ equations using the weighted nonlinear seemingly unrelated regression method. A leave-one-out cross-validation procedure was used to evaluate the predictive ability. The results revealed that stem biomass accounts for about two-thirds of the aboveground biomass. The ratio of wood biomass holds constant and that of branches increases with increasing D, H, CW and CL, while a reverse trend was found for bark and foliage. The root-to-shoot ratio nonlinearly decreased with D, ranging from 1.06 to 0.11. Tree diameter proved to be a good predictor, especially for root biomass. Tree height is more prominent than crown size for improving stem biomass models, yet it puts negative effects on crown biomass models with non-significant coefficients. Crown width could help improve the fitting results of the branch and foliage biomass models. We conclude that the selected generic biomass models for Mongolian oak and Liaodong oak will vigorously promote the accuracy of biomass estimation.

A Note on the Efficiency of Seemingly Unrelated Regression

1988 ◽  
Vol 42 (2) ◽  
pp. 137-139 ◽  
Author(s):  
James K. Binkley ◽  
Carl H. Nelson
Keyword(s):  
Seemingly Unrelated Regression ◽  
Unrelated Regression

Workplace disability and job satisfaction in Britain: A co-worker test?

2021 ◽  
pp. 0143831X2110142
Author(s):  
Getinet Astatike Haile
Keyword(s):  
Job Satisfaction ◽  
Negative Relationship ◽  
Organisational Culture ◽  
Seemingly Unrelated Regression ◽  
Unrelated Regression ◽  
Significant Negative Relationship ◽  
Using Data

The article examines the link between workplace disability (WD) and workplace job satisfaction (JS) using data from WERS2011. Controlling for a rich set of workplace characteristics including organisational culture, the study finds a significant negative relationship between JS and the share of disabled respondents within workplaces. Notably, Seemingly Unrelated Regression (SUR)-based analysis distinguishing between disabled and non-disabled respondents reveals that the negative relationship found is specific to non-disabled respondents. Moreover, disability equality policies are found to be significantly positively related with disabled respondents’ JS while they are negatively related with the JS of their non-disabled counterparts. The article ponders if there is a co-worker aspect to the WD–JS link and whether HR policies may need to take heed of co-worker dynamics in this respect.

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