In recent years, devices capable of linking the brain to the external world have been developed. Such devices directly measure the output of multiple neurons simultaneously. One obvious application of this technology is in helping those who are movement impaired; in theory it would be possible to implant such a device in the brain, and use its output to control movement of a robotic prosthetic limb, for instance. However, to achieve this goal, it is necessary to first understand the relationship between movement and neural signals. We consider data collected from rhesus monkeys in experiments, and propose a model for describing this relationship. The model generalizes several previously-considered models from the neuroscience literature, and allows individual neurons to (1) encode different kinematic variables, and (2) to have more general spike count distributions. The proposed model is used to decode cortical signals recorded for 258 neurons in the ventral premotor cortex of rhesus monkeys during an ellipse-drawing task, and we demonstrate that relative to the existing models, a substantial reduction in mean squared error is achieved.