Subgroup analysis for heterogeneous additive partially linear models and its application to car sales data

As an extension of additive partially linear model, heterogeneous additive partially linear model contains the homogeneous linear components and subject-dependent additive components, but has no group information of subject-dependent additive components. Such a model is more flexible and efficient for addressing some special issues such as precision medicine and precision marketing. A polynomial spline smoothing is used to approximate the heterogeneous additive components, and then a new clustering method is developed to automatically identify subgroups. The procedure avoids solving coefficient vector in each iterative step as in regression clustering procedures. Thus, this approach is rapid and computationally stable even if the sample size is large. Based on the clustered heterogeneous additive components, consistent estimators of the homogeneous parameters and subgroup-specific additive components are further obtained. Moreover, root n-consistency and asymptotic normality for the estimators of the parametric components are established. The simulation studies and real data analysis illustrate that the model and proposed clustering and estimation are effective in practice. (C) 2019 Elsevier B.V. All rights reserved.