Estimation for Longitudinal Varying Coefficient Partially Nonlinear Models Based on QR Decomposition

To address the estimation efficiency issues arising from multicollinearity and longitudinal data correlation in the varying coefficient partially nonlinear models (VCPNLM), a method based on QR decomposition and quadratic inference function (QIF) is proposed to obtain the orthogonality estimation of parameter components and varying coefficient functions. QR decomposition eliminates the pathology of the design matrix, and combines the adaptive weighting of the relevant structures within the group by QIF to effectively capture the complex correlation structure of longitudinal data. The theoretical analysis proves the asymptotic nature of the estimator, and the efficiency of the estimation method proposed in this paper is verified by simulation experiments.