带有交互项的广义部分函数型线性模型的应用
Application of Generalized Partially Function Type Linear Models with Interaction Terms
摘要: 随着科技的发展，数据信息逐渐呈现出多元化的特点，传统数据分析已经不能再满足人们的需求，因此越来越多的学者开始关注函数型数据分析。目前，函数型数据分析被应用到医学、气象学、环境学、经济学等各个领域。本文针对预测变量是函数型和标量型的混合变量，且考虑函数型预测变量之间的交互作用的情况，提出了一个带有交互项的广义部分函数型线性模型，利用主成分分析法对函数型预测变量进行降维处理，再运用加权最小二乘法对未知参数迭代求解，最后将此模型应用于粮食产量的研究中。研究结果表明：除特定时期外，降水量和气温在一定程度上均会促进粮食产量的增加，农作物总播种面积、农用机械总动力、化肥使用量对粮食产量的增加同样具有促进作用。
Abstract: With the development of technology, data information is gradually presenting more and more di-versified characteristics, traditional data analysis can no longer meet people’s needs, so more and more scholars are beginning to focus on functional data analysis. At present, functional data analy-sis has applications in a wide range of fields such as medicine, meteorology, environmental science and economics. In this paper, a generalized partially functional linear model with interaction terms is proposed for the case where the predictor variables are a mixture of functional and scalar varia-bles, and the interaction between the functional predictor variables is considered. The functional predictor variables are reduced in dimensionality using principal component analysis, and then the weighted least squares method is applied to iteratively solve for the unknown parameters. The re-sults of the study show that, except for certain periods, precipitation and temperature contribute to the increase in grain yield to a certain extent, and that the total area sown, total power of agricul-tural machinery and fertiliser use also contribute to the increase in grain yield.
文章引用：毛可敬, 李颂萱, 肖维维. 带有交互项的广义部分函数型线性模型的应用[J]. 应用数学进展, 2023, 12(6): 2781-2787. https://doi.org/10.12677/AAM.2023.126279

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