  Difficulties may arise when analyzing longitudinal data using mixed-effects
models if there are nonparametric functions present in the linear predictor
component. This study extends the use of semiparametric mixed-effects modeling
in cases when the response variable does not always follow a normal
distribution and the nonparametric component is structured as an additive
model. A novel approach is proposed to identify significant linear and
non-linear components using a double-penalized generalized estimating equation
with two penalty terms. Furthermore, the iterative approach provided intends to
enhance the efficiency of estimating regression coefficients by incorporating
the calculation of the working covariance matrix. The oracle properties of the
resulting estimators are established under certain regularity conditions, where
the dimensions of both the parametric and nonparametric components increase as
the sample size grows. We perform numerical studies to demonstrate the efficacy
of our proposal.
