SHIFT FUNCTION PLOTS FOR REGRESSION FITTING
Zilin Wang, David R. Bellhouse · 2004
Although a nonparametric regression model allows us to obtain a graphical display of the relationship between the response variable and the independent variables, the exact form of the regression function is not evident. This weakness can be overcome by a parametric model since the relationship between the dependent and the independent variables is specified mathematically. The objective of this paper is to introduce a new graphical approach, called the shift function plot, with which a hypothesis test is constructed to evaluate the goodness of fit of a parametric regression model. Under multi-stage stratified sampling schemes, we apply the shift function plots to survey data. Asymptotic properties of the survey estimator of the shift function are established. An empirical example from the 1990 Ontario Health Survey is used to illustrate the application of the shift function.