文章基本信息

标题：Estimating Semiparametric Varying Coefficients for Geographical Data in a Mixed Effects Model
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作者：Kenichi Satoh ; Tetsuji Tonda
期刊名称：JOURNAL OF THE JAPAN STATISTICAL SOCIETY
印刷版ISSN：1882-2754
电子版ISSN：1348-6365
出版年度：2014
卷号：44
期号：1
页码：25-41
DOI：10.14490/jjss.44.25
出版社：JAPAN STATISTICAL SOCIETY
摘要：A geographical weighted regression model can be used for visualizing or interpreting the covariate effects that vary with location. This model is usually estimated by a locally weighted regression or a kernel smoothing method, but we can regard the regression coefficients as varying linear coefficients that can be obtained from a global linear regression. There are two types of design vectors, one of which expresses linearity and the other is prepared for nonlinearity, i.e., it assumes a semiparametric surface with varying coefficients. Ridge estimators can then be used to suppress overfitting of the nonlinear part. With a mixed effects model, optimization of the ridge parameters and estimation of the regression parameters can be simultaneously executed. The linear structure of the varying coefficients then provides an asymptotic confidence interval as a function of location, but it is wider than a common pointwise confidence interval. We derive some tests for the varying coefficients and offer two examples using real data to illustrate our methodology. The results of the applied tests are summarized as the uniformity and the linearity of the varying coefficients.
关键词：Geographical weighted regression;mixed effects model;ridge parameter;semiparametric varying coefficient;simultaneous confidence interval