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基于非线性混合效应模型的柠条株高生长过程研究
许 昊,王占军,何建龙,等
作者单位
许 昊 宁夏大学 经济管理学院 
王占军 宁夏农林科学院 荒漠化治理研究所 
何建龙,等 宁夏农林科学院 荒漠化治理研究所 
摘要:
【目的】建立宁夏盐池地区柠条林株高生长量与种植年限关系模型,为精确掌握柠条林的生长过程提供依据。【方法】以盐池县北部、中部、南部的柠条林为研究对象,考虑不同地区立地条件的差异性及种植密度对株高生长的影响,对原有生长方程进行改进,并在改进的基础上利用非线性混合效应(NLME)模型方法建立其株高生长量与种植年限的关系模型,用幂函数、指数函数、常数加幂函数考虑数据间的异方差性,最后对NLME模型与传统模型、改进后的模型、不含随机效应的NLME模型的精度进行对比分析。【结果】相较其余3种模型,含有随机参数且考虑异方差结构的NLME模型精度有显著提高,其调整后的决定系数可达到0.986 5,平均绝对误差和剩余均方根误差分别为0.073 2和0.094 2。【结论】基于改进后Korf方程建立的柠条株高生长量与种植年限关系的NLME模型,考虑了种植密度对株高生长的影响,消除了数据间的异方差性,可准确描述盐池县不同地区柠条株高的生长过程。
关键词:  柠条  株高  生长过程  非线性混合效应模型  异方差
DOI:
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基金项目:宁夏农林科学院自主研发项目“宁夏干旱风沙区人工林固碳特征及固碳潜力研究”;宁夏自然科学基金项目(NZ14205);宁夏科技支撑计划项目“天然草场补播品种引选与改良及柠条科学利用技术集成研究”;宁夏大学引进人才科研项目“典型地区林业生态修复模式综合效益评估”(BQD2015010)
Height growth process of Caragana korshinskii based on nonlinear mixed effects models in Yanchi
XU Hao,WANG Zhanjun,HE Jianlong,et al
Abstract:
【Objective】In order to master the height growth process of Caragana korshinskii in Yanchi county,Ningxia,this paper built the height's growth and planting years relationship models.【Method】Improved model was built to consider the effects of planting densities and site conditions in Northern region,Middle region and Southern region according to the fitting data.Then,the nonlinear mixed effects (NLME) models approach was used to build the relationship models based on the improved model,considering the difference among the regions.Meanwhile,the Power function,Exponential function or the Constant plus Power function was added to remove the heteroscedasticity of the data,respectively.Finally,a precision comparison among the traditional model using the least square method,the improved model,the NLME model without random-effect parameters and the NLME model with random-effect parameters.【Result】The NLME model with random-effect parameters,considering heteroscedastic structure was significantly better than the others.The adjusted coefficient of determination,the absolute mean residual and the root mean square error for the NLME model with random-effect parameters were 0.986 5,0.073 2 and 0.094 2,respectively.【Conclusion】The NLME model with random-effect parameters based on the improved model could take the effect of the planting density into account and remove the heteroscedasticity of the data,and describe the height growth process accurately.
Key words:  Caragana korshinskii  height  growth process  nonlinear mixed effects models  heteroscedasticity