Varying Coefficient Regression Models: A Review and New Developments

Abstract

SummaryVarying coefficient regression models are known to be very useful tools for analysing the relation between a response and a group of covariates. Their structure and interpretability are similar to those for the traditional linear regression model, but they are more flexible because of the infinite dimensionality of the corresponding parameter spaces. The aims of this paper are to give an overview on the existing methodological and theoretical developments for varying coefficient models and to discuss their extensions with some new developments. The new developments enable us to use different amount of smoothing for estimating different component functions in the models. They are for a flexible form of varying coefficient models that requires smoothing across different covariates' spaces and are based on the smooth backfitting technique that is admitted as a powerful technique for fitting structural regression models and is also known to free us from the curse of dimensionality.

Robust varying coefficient model using L1 regularization

“…Another is to set each regression coefficient be function of different variables. There are various extensions of VCM ( Park et al ., 2015).…”

Varying coefficient modeling via least squares support vector regression

“…This model is gaining its popularity in statistics literature in recent years. The introductions, various applications and current research areas of the varying coefficient model can be found in [4,5,3,11]. Many areas of applied statistics have become aware of the problem of estimating varying coefficients and analyzing them appropriately.…”

“…There are various extensions of models. See [11] for details. Most literature has centered around the case that all regression coefficients are functions of a single vector of covariates.…”

Modeling heterogeneity: a praise for varying-coefficient models in causal analysis

“…The well-known time-varying-coefficient models for longitudinal data should be mentioned as well. For a recent review see Park et al (2015). The extension of (4) to (3) is just an extension of the classical nonparametric varying-coefficient model toward a non-or semiparametric mixed effects model, see for example González Manteiga et al (2013).…”