  In this paper, we consider the partially linear single-index models with
longitudinal data. To deal with the variable selection problem in this context,
we propose a penalized procedure combined with two bias correction methods,
resulting in the bias-corrected generalized estimating equation (GEE) and the
bias-corrected quadratic inference function (QIF), which can take into account
the correlations. Asymptotic properties of these methods are demonstrated. We
also evaluate the finite sample performance of the proposed methods via Monte
Carlo simulation studies and a real data analysis.
