This paper investigates the differences between single-vehicle and multi-vehicle truck crashes in New York City. The random parameter models take into account the time of day effect, the heterogeneous truck weight effect and other influencing factors such as crash characteristics, driver and vehicle characteristics, built environment factors and traffic volume attributes. Based on the results from the co-location quotient analysis, a spatial generalized ordered probit model is further developed to investigate the potential spatial dependency among single-vehicle truck crashes. The sample is drawn from the state maintained incident data, the publicly available Smart Location Data, and the BEST Practices Model (BPM) data from 2008 to 2012. The result shows that there exists a substantial difference between factors influencing single-vehicle and multi-vehicle truck crash severity. It also suggests that heterogeneity does exist in the truck weight, and it behaves differently in single-vehicle and multi-vehicle truck crashes. Furthermore, individual truck crashes are proved to be spatially dependent events for both single and multi-vehicle crashes. Last but not least, significant time of day effects were found for PM and night time slots, crashes that occurred in the afternoons and at nights were less severe in single-vehicle crashes, but more severe in multi-vehicle crashes.