On model diagnostics using varying coefficient models

Abstract

The paper motivates the use of varying coefficient models for diagnostics in regression models with continuous and factorial covariates. The varying coefficient model, which is restricted only by assumptions concerning the smoothness of the effects, is considered as the alternative to a parametric generalised linear model. Estimation is based on local likelihood smoothing and asymptotic properties of the estimators are derived. For the investigation of the discrepancy between the parametric model and the smooth alternative a simple graphical procedure is proposed. Moreover, tests are derived which allow for overall and componentwise investigation. The componentwise tests may be used to examine interaction effects of continuous and factorial regressors. Keywords:Generalised linear model; Local likelihood; Model diagnostic; Varying coefficient model.