非线性混合效应生长模型的拟合、随机效应预测和应变量预测间对应关系

Analysis and Comparison of Combinations among Fitting NLME and Predictors of Random Parameters and Response Variables

【目的】在非线性混合效应模型的拟合、随机效应预测和应变量预测3个环节上,常用一阶泰勒近似法将非线性模型线性化,泰勒近似的基点一般为随机效应参数的数学期望或迭代终值。在林业中,3个环节的基点常常并不完全一致,并可能影响预测精度。本研究以树高生长过程为例,分析了不一致的基点对预测精度的影响程度。【方法】以加拿大哥伦比亚省美国黄松解析木数据为基础,以三参数Logistic为基本模型,随机抽取49株用于拟合,30株用于验证。采用R语言的nlme函数和SAS的nlmixed过程拟合模型。nlme函数以随机效应的数学期望为基点,而nlmixed过程则以迭代终值为基点。利用SAS的IML过程预测随机效应与应变量,并计算预测精度。以预测误差均方(MSPE)、平均相对误差(MPE)、平均相对误差绝对值(MAPE)作为评价预测精度的指标。【结果】预测随机效应与预测应变量的基点不同,预测精度将大幅度下降。【结论】预测随机效应和预测应变量的基点必须一致,且仅需二者一致,与模型拟合的基点基本无关。如果二者一致,以数学期望或迭代终值为基点对预测精度基本上无显著影响;如果预测随机效应和预测应变量的基点不同,将显著降低预测精度。

【Objective】Fitting non-linear mixed effects models（ NLME）,predicting the random effects parameters,as well as predicting the response variable,often involve a Taylor series expansion for linearization,based upon either the expected value of the random effects or final iterative value. In forestry,however,the linearization bases are not always consistent as they should be,and probably reduced the accuracy of prediction. In this paper,we investigated the tree height growth and discussed the effects of inconsistency among the linearization bases for fitting,predicting random effects the response.【Method】We randomly selected 49 trees for NLME-fitting and 30 trees for validation from 79 dominant trees of ponderosa pine in British Columbia,Canada. The base model was three-parameter Logistic. We used the nlme function in R and the nlmixed procedure in SAS for model fitting,respectively corresponding linearization based upon the expected value and the final iterative value. The IML procedure in SAS was employed for predicting the random effects and the response. Mean squared prediction error（ MSPE）,mean percentage error（ MPE）,and mean absolute percentage error（ MAPE） were used as evaluation criteria.【Result】The results showed that inconsistent linearization bases between the random effects and the response significantly decreased the accuracy of the response prediction. 【Conclusion 】The linearization bases between the random effects and the response had to be consistent,and enough for obtaining predictionsas accurate as possible. The accuracy of prediction was invariant to the linearization base for model-fitting and to either the expected value or the final iterative value,which was used as a linearization base.