Partial Linear Regression Models for Clustered Data

This article considers the analysis of clustered data via partial linear regression models. Adopting the idea of modeling the within-cluster correlation from the method of generalized estimating equations, a least squares type estimate of the slope parameter is obtained through piecewise local polynomial approximation of the nonparametric component. This slope estimate has several advantages: (a) It attains n1/2-consistency without undersmoothing; (b) it is efficient when correct within-cluster correlation is used, assuming multivariate normality of the error; (c) the preceding properties hold regardless of whether or not the nonparametric component is of cluster level; and (d) this estimation method naturally extends to deal with generalized partial linear models. Simulation studies and a real example are presented in support of the theory.