Korean larch(Larix olgensis)is one of the main tree species for aff orestation and timber production in northeast China.However,its timber quality and growth ability are largely infl uenced by crown size,structure and...Korean larch(Larix olgensis)is one of the main tree species for aff orestation and timber production in northeast China.However,its timber quality and growth ability are largely infl uenced by crown size,structure and shape.The majority of crown models are static models based on tree size and stand characteristics from temporary sample plots,but crown dynamic models has seldom been constructed.Therefore,this study aimed to develop height to crown base(HCB)and crown length(CL)dynamic models using the branch mortality technique for a Korean larch plantation.The nonlinear mixed-eff ects model with random eff ects,variance functions and correlation structures,was used to build HCB and CL dynamic models.The data were obtained from 95 sample trees of 19 plots in Meng JiaGang forest farm in Northeast China.The results showed that HCB progressively increases as tree age,tree height growth(HT growth)and diameter at breast height growth(DBH growth).The CL was increased with tree age in 20 years ago,and subsequently stabilized.HT growth,DBH growth stand basal area(BAS)and crown competition factor(CCF)signifi cantly infl uenced HCB and CL.The HCB was positively correlated with BAS,HT growth and DBH growth,but negatively correlated with CCF.The CL was positively correlated with BAS and CCF,but negatively correlated with DBH growth.Model fi tting and validation confi rmed that the mixed-eff ects model considering the stand and tree level random eff ects was accurate and reliable for predicting the HCB and CL dynamics.However,the models involving adding variance functions and time series correlation structure could not completely remove heterogeneity and autocorrelation,and the fi tting precision of the models was reduced.Therefore,from the point of view of application,we should take care to avoid setting up over-complex models.The HCB and CL dynamic models in our study may also be incorporated into stand growth and yield model systems in China.展开更多
Nonlinear mixed effects model（NLMEM） is based on the relationship between the fixed and random effects in the regression function.The NLMEM has a competitive advantage in analyzing repeated measures data,the longitu...Nonlinear mixed effects model（NLMEM） is based on the relationship between the fixed and random effects in the regression function.The NLMEM has a competitive advantage in analyzing repeated measures data,the longitudinal data and multilevel data.This paper chose two kinds of two-level nonlinear mixed model to analyze basal area growth for Chinese Fir（Cunninghamia lanceolata）. Model 1 is a general two-level NLMEM and Model 2 is based on Model 1 to further consider the fixed effects parameters changes with a specific factor. Firstly,through the analysis of these two models, this paper defined the basic model to build the two-level NLMEM.Secondly,665 kinds of models derived from Model 1 and 2 703 kinds of models derived from Model 2 were calculated and compared. The results showed that:for Model 1,there were 57 kinds of models converging,and when the formal parameter b<sub>0</sub> considered the block effects and plot effects,b<sub>1</sub> and b<sub>4</sub> only considered the block effects, the model fitted the best;and for Model 2,there were 24 kinds of model converging,and when the formal parameter bs considered the block effects and plot effects,b<sub>1</sub> only considered block effects and the fixed effects b<sub>0</sub> changed with any level of block level, Model 2 fitted the best.Finally,by comparing the traditional nonlinear regression model,Model 1 and Model 2,the results showed that Model 1 and Model 2 fitted better than the traditional nonlinear regression, and Model 2 was best fitting model.展开更多
Nonlinear mixed effects model(NLMEM) is built on the relationship of the fixed and random effects in the regression function.The NLMEM has an obvious comparative advantage in analyzing the longitudinal data,repeated m...Nonlinear mixed effects model(NLMEM) is built on the relationship of the fixed and random effects in the regression function.The NLMEM has an obvious comparative advantage in analyzing the longitudinal data,repeated measures data and multilevel data.Two-level NLMEM is used to analyze the dominant height for Chinese fir (Cunninghamia lanceolata).The authors outline the two-level NLMEM and introduce the parameters estimation method of the model.Based on five common Richard and Logistic models,the mixed model is built.The modeling data are used to calculate and compare with 19 models derived from each based model,and 5 optimal mixed models are built.Compared the 5 optimal mixed models with traditional regression models,it is showed that the two-level NLMEM has a better fitting effect than the regression model.展开更多
Nonlinear mixed-eirects (NLME) modek have become popular in various disciplines over the past several decades.However,the existing methods for parameter estimation imple-mented in standard statistical packages such as...Nonlinear mixed-eirects (NLME) modek have become popular in various disciplines over the past several decades.However,the existing methods for parameter estimation imple-mented in standard statistical packages such as SAS and R/S-Plus are generally limited k) single-or multi-level NLME models that only allow nested random effects and are unable to cope with crossed random effects within the framework of NLME modeling.In t his study,wc propose a general formulation of NLME models that can accommodate both nested and crassed random effects,and then develop a computational algorit hm for parameter estimation based on normal assumptions.The maximum likelihood estimation is carried out using the first-order conditional expansion (FOCE) for NLME model linearization and sequential quadratic programming (SCJP) for computational optimization while ensuring positive-definiteness of the estimated variance-covariance matrices of both random effects and error terms.The FOCE-SQP algorithm is evaluated using the height and diameter data measured on trees from Korean larch (L.olgeiisis var,Chang-paienA.b) experimental plots aa well as simulation studies.We show that the FOCE-SQP method converges fast with high accuracy.Applications of the general formulation of NLME models are illustrated with an analysis of the Korean larch data.展开更多
A Bayesian analysis of the minimal model was proposed where both glucose and insulin were analyzed simultaneously under the insulin-modified intravenous glucose tolerance test (IVGTT). The resulting model was implemen...A Bayesian analysis of the minimal model was proposed where both glucose and insulin were analyzed simultaneously under the insulin-modified intravenous glucose tolerance test (IVGTT). The resulting model was implemented with a nonlinear mixed-effects modeling setup using ordinary differential equations (ODEs), which leads to precise estimation of population parameters by separating the inter- and intra-individual variability. The results indicated that the Bayesian method applied to the glucose-insulin minimal model provided a satisfactory solution with accurate parameter estimates which were numerically stable since the Bayesian method did not require approximation by linearization.展开更多
以湖南省黄丰桥国有林场103块样地共2461株杉木为例,建立单木冠幅模型。由于所调查数据是在不同立地条件下相同样地中重复观察得到,数据间存在明显相关性,为解决此问题,将考虑立地指数和样地对冠幅生长的随机影响,即建立嵌套2水平非线...以湖南省黄丰桥国有林场103块样地共2461株杉木为例,建立单木冠幅模型。由于所调查数据是在不同立地条件下相同样地中重复观察得到,数据间存在明显相关性,为解决此问题,将考虑立地指数和样地对冠幅生长的随机影响,即建立嵌套2水平非线性混合冠幅模型。从12个常用林分模型中选出较好的冠幅直径模型作为构建混合模型的基础模型。除胸高直径外,还考虑其他17个林分或树木因子对冠幅的影响。通过指标AIC(akaike information criterion)和对数似然确定最佳形式参数随机效应组合类型,用指数函数、幂函数以及常数加幂函数3种形式的残差方差模型消除异方差,最后对混合模型和传统回归模型进行比较及评价。结果表明:逻辑斯蒂形式的冠幅直径模型[模型(13)]拟合效果较好,选择为基础模型;胸径、冠底高、树高和样地优势高是影响冠幅的主要因子;幂函数消除异方差效果最好;与立地指数相比,立地指数与样地的嵌套效应对冠幅影响更大;模型(15)的嵌套2水平比总体平均水平和立地指数水平预测精度高,相比于模型(13)有明显改进。本文主要为方法研究,对于其他树种可以用相似方法构建冠幅模型。展开更多
基金supported by the National Key Research and Development Program of China(2017YFD0600401)the Fundamental Research Funds for the Central Universities(2572019CP08)
文摘Korean larch(Larix olgensis)is one of the main tree species for aff orestation and timber production in northeast China.However,its timber quality and growth ability are largely infl uenced by crown size,structure and shape.The majority of crown models are static models based on tree size and stand characteristics from temporary sample plots,but crown dynamic models has seldom been constructed.Therefore,this study aimed to develop height to crown base(HCB)and crown length(CL)dynamic models using the branch mortality technique for a Korean larch plantation.The nonlinear mixed-eff ects model with random eff ects,variance functions and correlation structures,was used to build HCB and CL dynamic models.The data were obtained from 95 sample trees of 19 plots in Meng JiaGang forest farm in Northeast China.The results showed that HCB progressively increases as tree age,tree height growth(HT growth)and diameter at breast height growth(DBH growth).The CL was increased with tree age in 20 years ago,and subsequently stabilized.HT growth,DBH growth stand basal area(BAS)and crown competition factor(CCF)signifi cantly infl uenced HCB and CL.The HCB was positively correlated with BAS,HT growth and DBH growth,but negatively correlated with CCF.The CL was positively correlated with BAS and CCF,but negatively correlated with DBH growth.Model fi tting and validation confi rmed that the mixed-eff ects model considering the stand and tree level random eff ects was accurate and reliable for predicting the HCB and CL dynamics.However,the models involving adding variance functions and time series correlation structure could not completely remove heterogeneity and autocorrelation,and the fi tting precision of the models was reduced.Therefore,from the point of view of application,we should take care to avoid setting up over-complex models.The HCB and CL dynamic models in our study may also be incorporated into stand growth and yield model systems in China.
文摘Nonlinear mixed effects model（NLMEM） is based on the relationship between the fixed and random effects in the regression function.The NLMEM has a competitive advantage in analyzing repeated measures data,the longitudinal data and multilevel data.This paper chose two kinds of two-level nonlinear mixed model to analyze basal area growth for Chinese Fir（Cunninghamia lanceolata）. Model 1 is a general two-level NLMEM and Model 2 is based on Model 1 to further consider the fixed effects parameters changes with a specific factor. Firstly,through the analysis of these two models, this paper defined the basic model to build the two-level NLMEM.Secondly,665 kinds of models derived from Model 1 and 2 703 kinds of models derived from Model 2 were calculated and compared. The results showed that:for Model 1,there were 57 kinds of models converging,and when the formal parameter b<sub>0</sub> considered the block effects and plot effects,b<sub>1</sub> and b<sub>4</sub> only considered the block effects, the model fitted the best;and for Model 2,there were 24 kinds of model converging,and when the formal parameter bs considered the block effects and plot effects,b<sub>1</sub> only considered block effects and the fixed effects b<sub>0</sub> changed with any level of block level, Model 2 fitted the best.Finally,by comparing the traditional nonlinear regression model,Model 1 and Model 2,the results showed that Model 1 and Model 2 fitted better than the traditional nonlinear regression, and Model 2 was best fitting model.
文摘Nonlinear mixed effects model(NLMEM) is built on the relationship of the fixed and random effects in the regression function.The NLMEM has an obvious comparative advantage in analyzing the longitudinal data,repeated measures data and multilevel data.Two-level NLMEM is used to analyze the dominant height for Chinese fir (Cunninghamia lanceolata).The authors outline the two-level NLMEM and introduce the parameters estimation method of the model.Based on five common Richard and Logistic models,the mixed model is built.The modeling data are used to calculate and compare with 19 models derived from each based model,and 5 optimal mixed models are built.Compared the 5 optimal mixed models with traditional regression models,it is showed that the two-level NLMEM has a better fitting effect than the regression model.
基金The authors would like to thank the Thirteenth Five-year Plan Pioneering project of High Technology Plan of the National Department of Technology (No. 2017YFC0504101)the National Natural Science Foundations of China (Nos. 31470641, 31300534 and 31570628) for the financial support of this study.
文摘Nonlinear mixed-eirects (NLME) modek have become popular in various disciplines over the past several decades.However,the existing methods for parameter estimation imple-mented in standard statistical packages such as SAS and R/S-Plus are generally limited k) single-or multi-level NLME models that only allow nested random effects and are unable to cope with crossed random effects within the framework of NLME modeling.In t his study,wc propose a general formulation of NLME models that can accommodate both nested and crassed random effects,and then develop a computational algorit hm for parameter estimation based on normal assumptions.The maximum likelihood estimation is carried out using the first-order conditional expansion (FOCE) for NLME model linearization and sequential quadratic programming (SCJP) for computational optimization while ensuring positive-definiteness of the estimated variance-covariance matrices of both random effects and error terms.The FOCE-SQP algorithm is evaluated using the height and diameter data measured on trees from Korean larch (L.olgeiisis var,Chang-paienA.b) experimental plots aa well as simulation studies.We show that the FOCE-SQP method converges fast with high accuracy.Applications of the general formulation of NLME models are illustrated with an analysis of the Korean larch data.
文摘A Bayesian analysis of the minimal model was proposed where both glucose and insulin were analyzed simultaneously under the insulin-modified intravenous glucose tolerance test (IVGTT). The resulting model was implemented with a nonlinear mixed-effects modeling setup using ordinary differential equations (ODEs), which leads to precise estimation of population parameters by separating the inter- and intra-individual variability. The results indicated that the Bayesian method applied to the glucose-insulin minimal model provided a satisfactory solution with accurate parameter estimates which were numerically stable since the Bayesian method did not require approximation by linearization.
文摘以湖南省黄丰桥国有林场103块样地共2461株杉木为例,建立单木冠幅模型。由于所调查数据是在不同立地条件下相同样地中重复观察得到,数据间存在明显相关性,为解决此问题,将考虑立地指数和样地对冠幅生长的随机影响,即建立嵌套2水平非线性混合冠幅模型。从12个常用林分模型中选出较好的冠幅直径模型作为构建混合模型的基础模型。除胸高直径外,还考虑其他17个林分或树木因子对冠幅的影响。通过指标AIC(akaike information criterion)和对数似然确定最佳形式参数随机效应组合类型,用指数函数、幂函数以及常数加幂函数3种形式的残差方差模型消除异方差,最后对混合模型和传统回归模型进行比较及评价。结果表明:逻辑斯蒂形式的冠幅直径模型[模型(13)]拟合效果较好,选择为基础模型;胸径、冠底高、树高和样地优势高是影响冠幅的主要因子;幂函数消除异方差效果最好;与立地指数相比,立地指数与样地的嵌套效应对冠幅影响更大;模型(15)的嵌套2水平比总体平均水平和立地指数水平预测精度高,相比于模型(13)有明显改进。本文主要为方法研究,对于其他树种可以用相似方法构建冠幅模型。
