中文摘要：

由于常用的线性混合效应模型对具有非线性关系的纵向数据建模具有一定的局限性,因此对线性混合效应模型进行扩展,根据变量间的非线性关系建立不同的非线性混合效应模型,并根据因变量的分布特征建立混合分布模型。基于一组实际的保险损失数据,建立多项式混合效应模型、截断多项式混合效应模型和B样条混合效应模型。研究结果表明,非线性混合效应模型能够显著改进对保险损失数据的建模效果,对非寿险费率厘定具有重要参考价值。

英文摘要：

Linear mixed effects models have some limitations to model longitudinal data with nonlinear relationship.The paper extends the linear mixed effects models,and based on the nonlinear relationship of variables and the distribution of dependent variable,different nonlinear mixed-effects regression models are established.Using a set of insurance loss data,the paper establishes polynomial mixed effects models,truncated polynomial mixed effects models and B-spline mixed effects models.The result shows that the nonlinear moixed effects models can significantly improve the prediction of the insurance loss.Models established in this paper extends the application of mixed-effects model,and has important value for nonlife insurance ratemaking.