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Model selection in multivariate semiparametric regression remains a challenge,especially for longitudinal data.We propose a model selection procedure that simultaneously selects fixed and random effects using a maximum penalized likelihood method with the adaptive least absolute shrink-age and selection operator(LASSO)penalty.We determine the correlation structure among multiple outcomes through random effects selection.Additionally,interactions of independent variables mod-eled by bivariate tensor product spline functions are selected using group LASSO.To implement the selection method,we propose a two-stage expectation-maximization(EM)procedure.We assess the operating characteristics of the proposed method through a simulation study.The method is illustrated in a clinical study of blood pressure development in children.