Estimation of neural models based on observed spike timing faces challenges as the amount of recorded units increases, especially when identifying detailed model features. Given that neural regions are generally sparsely connected, input selection is a critical step in model estimation but oftentimes computationally and theoretically challenging. In this paper, we detail an efficient methodology for estimating a sparse, nonlinear dynamical multiple-input, single-output model (MISO) applicable to large-scale (n > 50) single-unit recorded activity. The main contribution of this paper is the complete implementation of a principled group-lasso and local coordinate descent (LCD) algorithm into a generalized Volterra model (GVM) framework to achieve efficient sparse model estimation. Input selection is achieved with group-lasso by simultaneously selecting groups of parameters that are associated with each input. LCD yields efficient computation as the amount of inputs and parameters increase. We investigate and validate the performance of this estimation procedure with the application to a 64 input simulated model.