Model determination and estimation for the growth curve model via group SCAD penalty

The growth curve model is a useful tool for studying the growth problems, repeated measurements and longitudinal data. A key point using the growth curve model to fit data is determining the degree of polynomial profile form, choosing suitable explanatory variables, shrinking some regression coefficients to zero and estimating nonzero regression coefficients. In this paper, we propose a three-level variable selection approach based on weighed least squares with group SCAD penalty to handle the aforementioned problems. Considering the rows and columns of regression coefficient matrix as groups with overlap to control the polynomial order and variables, respectively, our proposed procedure enables us to simultaneously determine the degree of polynomial profile, identify the significant explanatory variables and estimate the nonzero regression coefficients. With appropriate selection of the tuning parameters, we establish the oracle property of the procedure and the consistency of the proposed estimation. We investigate the finite sample performances of our procedure in simulation studies whose results are very supportive, and also analyze a real data set to illustrate the usefulness of our procedure.