The accuracy of short-term traffic volume prediction in urban areas depends on the traffic volume characteristics and how prediction models address these characteristics. In this paper, we propose a space-time multivariate Negative Binomial (NB) regression for short-term traffic volume prediction in urban areas. The NB regression spatially correlates multiple overdispersed traffic volumes on multiple roads. We add the temporal correlation of volumes by allowing each volume to correlate with its values at previous time segments. Data consisting of traffic volumes collected in Taipei city are used to verify the model. The root mean square error is used to compare the proposed model with the Holt-Winters (HW) and Multivariate Structural Time series (MST) models. The results show that the proposed model is more accurate than the HW and MST models in all traffic conditions. The proposed model also determines causal interactions among spatial variables which assists in identifying roads affecting the prediction accuracy. Upstream roads are always significant, distant roads are always insignificant and downstream roads are significant during rush hours only.