Abstract
Varying coefficients, which might be varying on time, can be used for visualizations or interpretations of covariate effects. Varying coefficient surfaces, which might be varying on location, can be used for spatial data and useful for understanding geographical distribution of covariate effects. The estimator of varying coefficient surface is usually obtained by kernel smoothing methods. Since it is essentially the linear regression around fixed location,constructing a confidence interval or testing null hypothesis for a function of location is difficult.In this paper, we extend an estimating method on varying coefficients, proposed by Satoh and Yanagihara (2010), Satoh, Yanagihara and Kamo (2009), to varying coefficient surfaces using interaction model between covariates and bases on location. The proposed method can be applied for other complicated regression model, and can be easily calculated by the ordinary statistical software package. Other variables, such as measurement time and condition, can be used as a location information. Examples of analysis for spatial data and survival data were illustrated.
