Any regularization method requires the selection of a penalty parameter and many model selection criteria have been developed based on various discrepancy measures. Most of the attention has been focused on prediction mean squared error. In this paper we develop a model selection criterion based on regression parameter mean squared error via SURE (Stein’s unbiased risk estimator). We then apply this to the ${\ell _1}$ penalized least squares problem with grouped variables on over-determined systems. Simulation results based on topology identification of a sparse network are presented to illustrate and compare with alternative model selection criteria.