Nonlinear Seemingly Unrelated Regression Research Articles

An additive model system for heartwood, sapwood and bark diameter – A working example in Pinus koraiensis Siebold & Zucc. plantations

Accurate estimations of a tree stem’s heartwood diameter (HD), sapwood width (SW), bark thickness (BT) and diameter outside bark (DOB) are essential for volume and biomass calculations, forest management, and optimal timber production. Understanding these components also provides valuable insights into the ecological health and functioning of forest ecosystems. The additive model system, enhanced by machine learning algorithms, offers new tools for estimation. We constructed parametric taper models and nonparametric multilayer perceptron models to compare the accuracy of HD, SW, BT, and DOB estimates based on 3199 upper stem diameter measurements obtained from 103 sample Pinus koraiensis Siebold & Zucc. trees in Northeast China. In the context of the additive model system for tree stem internal components, we utilized nonlinear seemingly unrelated regression (NSUR) as a parametric method and multitask learning (MTL) as a nonparametric method. In the comparison of additive model systems, MTL (nonparametric) performed better than did NSUR (parametric) by improving the accuracy and generalizability of the stem and internal component estimates. The coefficient of determination (R2) for DOB, HD, SW, and BT increased by 0.31%, 1.39%, 4.21%, and 4.31%, respectively. Based on these results, we conclude that the MTL provides a valid option for improving HD, SW, BT, and DOB and enhancing the volume prediction of stem components.

Tree Biomass Modeling Based on the Exploration of Regression and Artificial Neural Networks Approaches

Understanding the dynamics of tree biomass is a significant factor in forest ecosystems, and accurate quantitative knowledge of its development provides support for the optimization of forest management. This work aimed to employ innovative practices in tree biomass modeling, artificial neural network approaches along with the least-squares regression methodology, in order to construct reliable and accurate estimation and prediction models that contribute to solving the emerging problems in the field of sustainable forest management. Based on this aim, different modeling strategies were developed and explored. The nonlinear seemingly unrelated regression (NSUR) methodology, the generalized regression (GRNN), the resilient propagation (RPNN) and the Bayesian regularization (BRNN) artificial neural network algorithms were utilized for the construction of reliable biomass models to attain the most accurate and reliable tree biomass components and total tree biomass estimations. The work showed that GRNN models provided a significantly better performance compared with the other modeling methodologies tested. Considering the non-parametric nature of the GRNN neural network algorithm, the fact that it was designed for nonlinear regression-type problems capable of dealing with small datasets, this modeling approach warrants consideration as an effective alternative to nonlinear regression or to other neural network approaches to the field of tree biomass modeling.

An Alternative Method for Estimation of Stand-Level Biomass for Three Conifer Species in Northeast China

Accurate large-scale biomass prediction is crucial for assessing forest carbon storage and dynamics. It can also inform sustainable forest management practices and climate change mitigation efforts. However, stand-level biomass models are still scarce worldwide. Our study aims to introduce the generalized additive model (GAM) as a convenient and efficient approach for forest biomass estimation. Data from 311 sample plots of three conifer species in northeastern China were used to evaluate the performance of the GAM model and compare it with traditional nonlinear seemingly unrelated regression (NSUR) models in predicting stand biomass, including total, aboveground, and component biomass. The results indicated that the goodness of fit of GAM was better than that of NSUR in two model systems. In the majority of cases, the scatter plots and prediction performance revealed that the stand total and component biomass models utilizing GAM outperformed those based on NSUR. Disregarding heteroscedasticity and requiring fewer statistical assumptions provide additional support for the replacement of NSUR-based models with GAM-based models. This study implies that the GAM approach has greater potential for developing a system of stand biomass models.

Biomass allometric models for Larix rupprechtii based on Kosak's taper curve equations and nonlinear seemingly unrelated regression.

The diameter at breast height (DBH) is the most important independent variable in biomass allometry models based on metabolic scaling theory (MST) or geometric theory. However, the fixed position DBH can be misleading in its use of universal scaling laws and lead to some deviation for the biomass model. Therefore, it is still an urgent scientific problem to build a high-precision biomass model system. A dataset of 114 trees was destructively sampled to obtain dry biomass components, including stems, branches, and foliage, and taper measurements to explore the applicability of biomass components to allometric scaling laws and develop a new system of additive models with the diameter in relative height (DRH) for each component of a Larch (Larix principis-rupprechtii Mayr) plantation in northern China. The variable exponential taper equations were modelled using nonlinear regression. In addition, applying nonlinear regression and nonlinear seemingly unrelated regression (NSUR) enabled the development of biomass allometric models and the system of additive models with DRH for each component. The results showed that the Kozak's (II) 2004 variable exponential taper equation could accurately describe the stem shape and diameter in any height of stem. When the diameters in relative height were D0.2, D0.5, and D0.5 for branches, stems, and foliage, respectively, the allometric exponent of the stems and branches was the closest to the scaling relations predicted by the MST, and the allometric exponent of foliage was the most closely related to the scaling relations predicted by geometry theory. Compared with the nonlinear regression, the parameters of biomass components estimated by NSUR were lower, and it was close to the theoretical value and the most precise at forecasting. In the study of biomass process modelling, utilizing the DRH by a variable exponential taper equation can confirm the general biological significance more than the DBH of a fixed position.

Sensitivity of Stand-Level Biomass to Climate for Three Conifer Plantations in Northeast China

The accurate assessment of forest biomass is vital to climate change mitigation. Based on forest survey data, stand biomass models can effectively assess forest biomass carbon at large scales. However, traditional stand biomass models have ignored the potential effects of the climate on stand biomass estimation. There is still a lack of research on whether or not and in what ways the effects of the climate reduce uncertainty in biomass estimation and carbon accounting. Therefore, two types of stand biomass models, including basic stand biomass models (BBMs) and climate-sensitive stand biomass models (CBMs), were developed and tested using 311 plantation plots of Korean pine (Pinus koraiensis Siebold & Zucc.), Korean larch (Larix olgensisi A. Henry), and Mongolian pine (Pinus sylvestris var. mongolica Litv.) in Northeast China. The two types of models were developed by applying simultaneous equations based on nonlinear, seemingly unrelated, regression (NSUR) to ensure additivity of the stand total and components biomass (root, stem, branch, and needle). The results of fitting and leave-one-out cross-validation (LOOCV) indicated that the CBMs performed better than the corresponding BBMs. The RMSEs of the stand total biomass decreased by 3.5% to 10.6% for the three conifer species. The influence of temperature-related climate variables on the biomass of stand components was greater than that of precipitation-related climate variables. The sensitivity of the three conifer species to climate variables was ranked as Korean pine > Mongolian pine > Korean larch. This study emphasizes the importance of combining climate variables in stand biomass models to reduce the uncertainty and climate effects in forest biomass estimation, which will play a role in carbon accounting for forest ecosystems.

Compatible Biomass Model of Moso Bamboo with Measurement Error

Moso bamboo is characterized by its fast growth and high yield and is important as a carbon sink species. Therefore, understanding the biomass distribution of its components is crucial. Based on the measured individual biomass data of 66 Phyllostachys heterocycla cv. Pubescens plants in the Yixing state-owned forest in Jiangsu Province, nonlinear simultaneous equations with measurement errors were constructed using nonlinear error-in-variable models (NEIVM) (one step, two step) and nonlinear seemingly unrelated regression (NSUR). Variables affecting biomass were evaluated, including diameter at breast height (DBH), bamboo height (H), height to crown base (HCB), node length at DBH (NL), base diameter (BD), and bamboo age (A). DBH, H, and HCB had significant effects on the biomass of each component. They were used to construct a one-predictor system using DBH, a two-predictor system using DBH and H, and a three-predictor system using DBH, H, and HCB. Regardless of the number of variables used, the fitting accuracy of the NEIVM one-step method exceeded that of the two-step method, and that of NEIVM exceeded that of NSUR estimation. As a system using three predictive variables is better than other systems, we recommend using the one-step NEIVM method for Moso bamboo biomass estimation.

Simultaneous Compatible System of Models of Height, Crown Length, and Height to Crown Base for Natural Secondary Forests of Northeast China

Individual trees are characterized by various sizes and forms, such as diameter at breast height, total height (H), height to crown base (HCB), crown length (CL), crown width, and crown and stem forms. Tree characteristics are strongly related to each other, and studying their relationships is very important. The knowledge of the compatibility and additivity properties of the major tree characteristics, such as H, CL, and HCB, is essential for informed decision-making in forestry. H can be used to represent site quality and CL represents biomass and photosynthesis of crown, which is the performance of individual tree vigor and light interception, and the longer the crown length (or shorter HCB) is, the more vigorous the tree would be. However, none of the studies have uncovered their inherent relationships quantitatively. This study attempts to explore such relationships through the application of appropriate modeling approaches. We applied seemingly unrelated regression, such as nonlinear seemingly unrelated regression (NSUR), which is commonly used for exploring the compatibility and additivity properties of the variables, for the proposes. The NSUR involves the variance and covariance matrices of the sub-models that are used for the interpretation of the correlations among the variables of interest. The data set acquired from Mongolian oak forest and spruce-fir forest in the Jingouling forest farm of the Wangqing Forest Bureau in the Northeast of China were used to construct two types of model systems: a compatible model system (the model system of H, CL, and HCB can be estimated simultaneously) and an additive model system (the sum of HCB and CL is H, the form of the H sub-model equals the sum of the HCB and CL sub-models) from the individual models of H, CL, and HCB. Among the various tree-level and stand-level variables evaluated, D (diameter at breast), Dg (quadratic mean diameter), DT (dominant diameter), CW (crown width), SDI (stand density index), and BAS (basal area of stand) contributed significantly highly to the variations of the response of the variables of interest in the model systems. Modeling results showed the existence of the compatibility and additivity of H, CL, and HCB simultaneously. The additive model system exhibited better fitting performance on H and HCB but poorer fitting on CL compared with the simultaneous model system, indicating that the performance of the additive model system could be higher than that of the simultaneous model system. Model tests against the validation data set also confirmed such results. This study contributes a novel approach to solving the compatibility and additivity of the problems of H, CL, and HCB models through the application of the robust estimating method, NSUR. The results and algorithm presented will be useful for constructing similar compatible and additive model systems of multiple tree-level models for other tree species.

Regression estimators for aboveground biomass and its constituent parts of trees in native southern Brazilian forests

The mathematical models used applying the Nonlinear Seemingly Unrelated Regressions (NSUR) or Weighted Nonlinear Seemingly Unrelated Regressions (WNSUR) methodologies can contribute to generate acceptable and reliable estimates of total aboveground biomass and its constituent parts, which are needed to implement forest management strategies to maintain desirable and sustainable carbon stocks. The aim of this study was: 1) to fit the sample data with independent nonlinear regression models and present the results obtained from the respective statistical estimates for total biomass aboveground and the constituent parts of trees in native forest trees. 2) To fit the sample data with regression models simultaneously, that is, whose models are composed of appropriate combinations of their coefficients, in order to obtain additivity of the estimates and present better results for the total aboveground biomass and the constituent parts of the trees. 3) To apply weighting procedures to the variances of the fitted models. 4) To evaluate the error due to the regression function on forest biomass estimation. The data came from eight sites located in the states of Parana and Rio Grande do Sul, Brazil, and information was collected on diameter at 1.30 m aboveground (DBH), total height, biomasses of the trunk components (branches and leaves) and total aboveground biomass. Non-linear functions were independently and simultaneously fitted, using DBH and total height as independent variables in the regression models. Independent fitting of equations was performed using generalized nonlinear least squares (ENGLS) and simultaneous fitting of equations was obtained by means of NSUR. Weighting, by applying a variance structure in the two procedures, was done to solve the issue of heteroscedasticity. Numerically, the equations fitted simultaneously performed better and were more efficient than the independently fitted models, which resulted in biological inconsistency, that is, non-additivity of the biomass of constituent parts of the trees and the total biomass. Simultaneous fitting generated superior statistical and biological properties to obtain tree estimates of the of constituent parts of the trees and total aboveground biomass in native forests of southern Brazil. The smaller error due to the regression function used in the forest biomass inventory was obtained by simultaneous fitting. With these results, the procedure using simultaneous and weighted fitting of equations (WNSUR) is recommended to fit biomass equations for native forests in southern Brazil.

Additivity of stand basal area predictions in canopy stratifications for natural oak forests

Stand basal area is an important variable for evaluating forest productivity. In this study, four types of growth models were used for modeling the stand basal area of natural oak forests in Hunan Province, China. The results showed that the Schumacher model (Eq. (3)) performed the best. Because of different canopy layers in natural oak secondary forests, it is important to develop stand basal area models considering canopy stratification. Three widely used canopy stratification methods were used for natural oak forests: the clustering analysis of tree height, classification scheme of the International Union of Forest Research Organizations (IUFRO) standard, and canopy competition cut-off height (CCH) method. According to the standards set forth in the National Standards of the People’s Republic of China (GB/T 26424-2010), the forests were divided into two layers: upper and lower. Among the three canopy stratification approaches, the IUFRO method was selected as the best. In addition, it should be noted that the sum of the basal area predictions at different layers can generate inconsistent results, as compared to predictions from the total stand basal area model. To solve the additivity of stand basal area predictions, the additive stand basal area growth model was established by nonlinear seemingly unrelated regression (NSUR). Comparing with the whole stand basal area growth model without stratification, the R2 values of basal area growth models with stratification increased by 4.78% (from 0.9277 to 0.9721). In addition, compared with equations estimated separately, the NSUR method increased R2 by 0.82% (from 0.9721 to 0.9801). The results reveal that the NSUR method can be applied to solve the additivity of stand basal area predictions at each layer and can improve model precision, which provides helpful insights into developing stand growth models in natural forests.

Identification and estimation of the SEIRD epidemic model for COVID-19

This paper studies the SEIRD epidemic model for COVID-19. First, I show that the model is poorly identified from the observed number of deaths and confirmed cases. There are many sets of parameters that are observationally equivalent in the short run but lead to markedly different long run forecasts. Second, I show that the basic reproduction number R0 can be identified from the data, conditional on epidemiologic parameters, and propose several nonlinear SUR approaches to estimate R0. I examine the performance of these methods using Monte Carlo studies and demonstrate that they yield fairly accurate estimates of R0. Next, I apply these methods to estimate R0 for the US, California, and Japan, and document heterogeneity in the value of R0 across regions. My estimation approach accounts for possible underreporting of the number of cases. I demonstrate that if one fails to take underreporting into account and estimates R0 from the reported cases data, the resulting estimate of R0 may be biased downward and the resulting forecasts may exaggerate the long run number of deaths. Finally, I discuss how auxiliary information from random tests can be used to calibrate the initial parameters of the model and narrow down the range of possible forecasts of the future number of deaths.

Allometric models for above and below-ground biomass of wild Musa stands in tropical semi evergreen forests

Wild Musa species constitute an important component of tropical rain forests, wet evergreen forests and deciduous forests. Unlike forest trees, biomass estimation models are virtually lacking for wild Musa species. The present study aimed to determine whether growth and biomass accumulation in Musa species follow simple allometric scaling rules; and to develop allometric models for estimation of biomass storage in wild Musa balbisiana stands. A total of 156, M. balbisiana plants were harvested for above and below ground biomass for developing the biomass estimation models. The commonly used height-diameter (H-D) models: Chapman-Richard, exponential, Gompertz, hyperbolic, Michaelis-Menten (saturation growth), power-law, Weibull and Von Bertalanffy functions were used to predict missing heights from field measurement of plant diameter. The performance of the power-law model involving D alone, pseudo-stem height (Hp) alone or a combination of D and Hp was used to develop the best biomass estimation model. Nonlinear seemingly unrelated regression (NSUR) was used to model total biomass stocks. The stand density and basal area of the wild Musa stand was 14900 pseudo-stem ha−1, and 14.94 m2 ha−1, respectively. Based on the goodness of fit criteria, Hp, and D at 130 cm, the Exponential and Gompertz functions were observed to be the two best models for describing H-D relationship. A model containing D and Hp was found to be the best model for total biomass estimation in M. balbisiana. The total biomass stock predicted by our best NSUR model was 90.7 Mg ha−1, of which 55.4 Mg ha−1 was found in above-ground and 34.7 Mg ha−1 in below-ground plant parts. The present study suggests wild M. balbisiana hold significant potential to contribute to stand level biomass stock in forest ecosystems where they occur mixed with trees.

Prediction of Individual Tree Diameter and Height to Crown Base Using Nonlinear Simultaneous Regression and Airborne LiDAR Data

The forest growth and yield models, which are used as important decision-support tools in forest management, are commonly based on the individual tree characteristics, such as diameter at breast height (DBH), crown ratio, and height to crown base (HCB). Taking direct measurements for DBH and HCB through the ground-based methods is cumbersome and costly. The indirect method of getting such information is possible from remote sensing databases, which can be used to build DBH and HCB prediction models. The DBH and HCB of the same trees are significantly correlated, and so their inherent correlations need to be appropriately accounted for in the DBH and HCB models. However, all the existing DBH and HCB models, including models based on light detection and ranging (LiDAR) have ignored such correlations and thus failed to account for the compatibility of DBH and HCB estimates, in addition to disregarding measurement errors. To address these problems, we developed a compatible simultaneous equation system of DBH and HCB error-in-variable (EIV) models using LiDAR-derived data and ground-measurements for 510 Picea crassifolia Kom trees in northwest China. Four versatile algorithms, such as nonlinear seemingly unrelated regression (NSUR), two-stage least square (2SLS) regression, three-stage least square (3SLS) regression, and full information maximum likelihood (FIML) were evaluated for their estimating efficiencies and precisions for a simultaneous equation system of DBH and HCB EIV models. In addition, two other model structures, namely, nonlinear least squares with HCB estimation not based on the DBH (NLS and NBD) and nonlinear least squares with HCB estimation based on the DBH (NLS and BD) were also developed, and their fitting precisions with a simultaneous equation system compared. The leave-one-out cross-validation method was applied to evaluate all estimating algorithms and their resulting models. We found that only the simultaneous equation system could illustrate the effect of errors associated with the regressors on the response variables (DBH and HCB) and guaranteed the compatibility between the DBH and HCB models at an individual level. In addition, such an established system also effectively accounted for the inherent correlations between DBH with HCB. However, both the NLS and BD model and the NLS and NBD model did not show these properties. The precision of a simultaneous equation system developed using NSUR appeared the best among all the evaluated algorithms. Our equation system does not require the stand-level information as input, but it does require the information of tree height, crown width, and crown projection area, all of which can be readily derived from LiDAR imagery using the delineation algorithms and ground-based DBH measurements. Our results indicate that NSUR is a more reliable and quicker algorithm for developing DBH and HCB models using large scale LiDAR-based datasets. The novelty of this study is that the compatibility problem of the DBH model and the HCB EIV model was properly addressed, and the potential algorithms were compared to choose the most suitable one (NSUR). The presented method and algorithm will be useful for establishing similar compatible equation systems of tree DBH and HCB EIV models for other tree species.

Origin-based biomass allometric equations, biomass partitioning, and carbon concentration variations of planted and natural Larix gmelinii in northeast China

The area of larch (Larix gmelinii) plantations in northeast China has increased following the massive afforestation program implemented by China’s central government to provide biomass for global carbon sink and the development of industrial sectors. Hence, a better comprehension of equations used to characterize the estimation of regional biomass is much needed. A total of 301 sample trees of both planted and natural larch from northeast China were used to construct the additive systems of general and dummy variable models using weighted nonlinear seemingly unrelated regression (NSUR) to investigate the effect of forest origin on tree compartments and total biomass equations. Three different combinations of predictors were used in the two additive systems, and each biomass equation has its own specific weighting function to achieve the homoscedasticity in model residuals. Biomass partitioning, root-to-shoot ratio (RSR), and carbon concentration between the two origins were also analyzed. The results indicated that (1) the additive system of origin-based dummy variable model clearly outperformed the general additive model according to their respective predictors’ combinations and the difference between them were found to be significant; (2) based on the jackknife models’ validation, the two additive systems delivered good biomass predictions, of which the best models’ R2 were 0.939, 0.987, 0.910, 0.878, and 0.989 for root, stem, branch, foliage, and total biomass equations, respectively; (3) biomass allocations were varied between the two origins, and the RSR was higher in natural forests (0.32 ± 0.16) compared to plantations (0.25 ± 0.06) both averagely (±SD) and entirely across all diameter classes; (4) the mean carbon concentrations of root, stem, branch, and foliage observed in naturally regenerated trees were 1.81%, 2.90%, 1.23%, and 2.30% higher than those in plantations, respectively. The newly developed additive systems of origin-based equations can provide a more precise estimation for single-tree biomass of Larix gmelinii in China’s National Forest Inventory.

Aggregated Biomass Model Systems and Carbon Concentration Variations for Tree Carbon Quantification of Natural Mongolian Oak in Northeast China

Three systems of additive biomass models were developed and the effects of tree components, tree sizes, and tree growing regions on the carbon concentration were analyzed for Mongolian oak (Quercus mongolica Fisch. ex Ledeb.) in the natural forests of Northeastern China. The nonlinear seemingly unrelated regression (NSUR) method was used to fit each of the three systems simultaneously; namely, aggregated model systems with no parameter restriction (AMS0), aggregated model systems with one parameter restriction (AMS1), and aggregated model systems with three parameter restrictions (AMS3). A unique weighting function for each biomass model was applied to address the heteroscedasticity issue. The systems assertively guarantee the additivity property, in which, the summation of the respective predicted tree components (i.e., root, stem, branch, and foliage) will match the prediction of subtotals (i.e., crown and aboveground) and total biomass. Using one-, two-, and three-predictor combinations (i.e., D (diameter at breast height), D and H (total height), and D, H, and CL (crown length)) as the general model underlying formats, three systems of additive biomass model were developed. Our results indicate that (1) all of the aggregated model systems performed well and the differences between the systems were relatively small; (2) the rank order of the three systems based on an array of statistics are as follows: AMS0 > AMS1 > AMS3; (3) the carbon concentration significantly varied depending on the types of tree tissues and growing regions; (4) the regional respective component carbon concentration and regional weighted mean carbon concentration multiplied by observed biomass value appeared to be the best approach to calculate carbon stock.

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

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.

Food Consumption Patterns and Demand Elasticities for South West Rural Ethiopia

Demand elasticities are powerful tools to quantify welfare effects of relative price changes concomitant to shocks in economic environment of consumers. This study examined food demand elasticities to demonstrate how rural households in South West Ethiopia react to income and price changes by drawing on 267 observations of Household Income and Consumption Expenditure Survey data collected by Central Statistical Authority. It estimated Quadratic Almost Ideal Demand Systems (QUAIDS) of six groups of food items controlled for censoring and expenditure endogeneity by applying Nonlinear Seemingly Unrelated Regression (NLSUR) technique after incorporating household characteristics into the systems as intercept shifters. The descriptive statistics results showed that households allocate about 55 percent of income to food consumption of which root crops, fruits and vegetables were the dominant. The inferential statistics revealed that household characteristics such as sex, family size, age, education and location significantly influence the consumption patterns, and changes in income and prices would induce adjustment in consumption patterns that manifest by change in the quantities and types of items consumed. The results implicate the need for emphasizing crop specific price policies over holistic approach and policies that target income over policies targeting prices.

On (the Lack of) Identification of the SEIRD Epidemic Model for COVID-19, Its Estimation, and Related Problems

This paper studies the SEIRD epidemic model for COVID-19. First, I show that the model is poorly identified from the observed number of deaths and confirmed cases. There are many sets of parameters that are observationally equivalent in the short run but lead to markedly different long run forecasts. Second, I show that the basic reproduction number R0 can be identified from the data, conditional on epidemiologic parameters, and propose several nonlinear SUR approaches to estimate R0. I study the performance of these methods using Monte Carlo studies and demonstrate that they yield fairly accurate estimates of R0. Next, I apply these methods to estimate R0 for the US, California, and Japan, and document heterogeneity in the value of R0 across regions. My estimation approach accounts for possible underreporting of the number of cases. I demonstrate that if one fails to take underreporting into account and estimates R0 from the reported cases data, the resulting estimate of R0 may be biased downward and the resulting forecasts may exaggerate the long run number of deaths. Finally, I discuss how auxiliary information from random tests can be used to calibrate the initial parameters of the model and narrow down the range of possible forecasts of the future number of deaths.

ADDITIVITY OF VOLUME COMPONENTS OF TREE BOLES

Bark volume and inside-bark volume are components of tree boles. Thus, equations for volume components must be additive so that their estimates are compatible to the total volume. This research aimed to present a method based on the additivity principle such that this condition is met. Volume modeling was performed using data from black-wattle ( Acacia mearnsii De Wild.) stands. We treat the inside-bark volume and bark volume as components of bole volume. The method known as Nonlinear Seemingly Unrelated Regressions (NSUR) ensured the condition for which the component values estimated by means of non-linear equations were additive and equivalent to the total value, demonstrating that the method is appropriate.

Variation in Carbon Concentration and Allometric Equations for Estimating Tree Carbon Contents of 10 Broadleaf Species in Natural Forests in Northeast China

In this study, the effects of tree species, tissue types, and tree size on the carbon concentration were studied, and the two additive systems, one with tree diameter (D), and the other with both D and tree height (H), were developed to estimate the stem, root, branch, and foliage carbon content of 10 broadleaf species in northeast China. The coefficients of the two systems were estimated with the nonlinear seemingly unrelated regression (NSUR), while the heteroscedasticity of the model residual was solved with the weight function. Our results showed that carbon concentrations varied along with tree species and size; the tissues and foliage contained higher carbon concentration than other observed tissues. The two additive carbon equation systems exhibited good predictive and fitting performance, with Ra2 > 0.87, average prediction error of approximately 0, and small average absolute error and absolute error percentage. The carbon equation system constructed with D and H exhibited better fit and performance, particularly for the stem and total carbon. Thus, the additive carbon equation systems estimated the tree carbon of 10 broadleaf species more accurately. These carbon equations can be used to monitor the carbon pool sizes for natural forests in the Chinese National Forest Inventory.

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

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.