In the mammalian neocortex, there is a high diversity of neuronal types. To facilitate construction of system models with multiple cell types, we generate a database of point models associated with the Allen Cell Types Database. We construct a series of generalized integrate-and-fire (GLIF) models of increasing complexity aiming to reproduce the spiking behaviors of the recorded neurons. We test the performance of these GLIF models on data from 771 neurons from 14 transgenic lines, with increasing model performance for more complex models. To answer how complex a model needs to be to reproduce the number of electrophysiological cell types, we perform unsupervised clustering on the parameters extracted from these models. The number of clusters is smaller for individual model types, but when combining all GLIF parameters 18 clusters are obtained, while 11 clusters are obtained using 16 electrophysiological features. Therefore, these low dimensional models have the capacity to characterize the diversity of cell types without the need for a priori defined features.