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目的 放宽经典线性模型中的多个解释变量的线性假定和探讨多维样条回归分析模型。方法 利用最小惩罚二乘原理构造惩罚残差平方和 ,通过广义交互有效得分函数自动选择光滑参数值 ,对有关矩阵进行QR分解、Cholesky分解以及奇异值分解。 结果 用SAS程序实现了多维样条回归分析 ,得到了模型系数向量和多维样条函数的最小惩罚二乘估计 ,实例分析表明 ,多维样条回归模型较一般线性模型有更强的适应性。结论 多维样条回归模型是一般线性模型的全面扩展 ,为探索医学指标间的关系以及进行预测提供了可靠的线索和有效的途径。
Aim To relax the linear assumption of multiple explanatory variables in the classical linear model and to explore the multi-dimensional spline regression analysis model. The method constructs the sum of squared residuals by using the principle of least penalty multiplication. The smooth parameter values are automatically selected by the generalized reciprocal effective score function, and QR decomposition, Cholesky decomposition and singular value decomposition of the related matrix are performed. Results The multi-dimensional spline regression analysis was implemented with the SAS program, and the least-squares two-way estimation of the model coefficient vector and the multidimensional spline function was obtained. The case analysis shows that the multi-dimensional spline regression model has stronger adaptability than the general linear model. Conclusions Multidimensional spline regression model is a general extension of the general linear model, which provides reliable clues and effective ways to explore the relationship between medical indicators and predict them.