Varying Index Coefficient Models
Varying Index Coefficient Models
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DOI：
10.1080/01621459.2014.903185
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发表时间：
2015-03-01
影响因子：
3.7
通讯作者：
Song, Peter X. -K.
中科院分区：
文献类型：
--
作者：
Ma, Shujie;Song, Peter X. -K.
在回归分析中使用交互作用来研究协变量效应对响应变量的影响已经有很长的历史。在本文中，我们的目标是解决由于在复杂数据的回归模型中包含这种高阶效应而产生的两种新挑战。第一类涉及单个协变量的相互作用作用弱而组合协变量的相互作用作用强的情况，另一类涉及由低作用协变量指导的非线性相互作用作用的存在。我们提出了一类新的具有变指标系数的半参数模型，使我们能够建模和评估组协变量之间的非线性相互作用对响应变量的影响。因此，大多数现有的半参数回归模型都是我们所提出模型的特殊情况。我们利用轮廓最小二乘法和局部拟合开发了一种数值稳定且计算速度快的估计方法。我们建立了指标系数估计量的估计相合性和渐近正态性，以及非参数函数估计量的oracle性质。此外，还提供了广义似然比检验来检验是否存在相互作用效应或是否存在非线性相互作用效应。我们的模型和估计方法通过模拟研究和对儿童生长数据的分析来说明，以评估母亲在怀孕期间暴露于内分泌干扰化合物所引起的生长速率的变化。本文的补充材料可在网上获得。
It has been a long history of using interactions in regression analysis to investigate alterations in covariate-effects on response variables. In this article, we aim to address two kinds of new challenges arising from the inclusion of such high-order effects in the regression model for complex data. The first kind concerns a situation where interaction effects of individual covariates are weak but those of combined covariates are strong, and the other kind pertains to the presence of nonlinear interactive effects directed by low-effect covariates. We propose a new class of semiparametric models with varying index coefficients, which enables us to model and assess nonlinear interaction effects between grouped covariates on the response variable. As a result, most of the existing semiparametric regression models are special cases of our proposed models. We develop a numerically stable and computationally fast estimation procedure using both profile least squares method and local fitting. We establish both estimation consistency and asymptotic normality for the proposed estimators of index coefficients as well as the oracle property for the nonparametric function estimator. In addition, a generalized likelihood ratio test is provided to test for the existence of interaction effects or the existence of nonlinear interaction effects. Our models and estimation methods are illustrated by simulation studies, and by an analysis of child growth data to evaluate alterations in growth rates incurred by mother's exposures to endocrine disrupting compounds during pregnancy. Supplementary materials for this article are available online.