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We propose a novel approach to network-based event likelihood modeling that estimates the probabilities of event occurrences on a network and identifies the influences of site and situation characteristics. Our premise is that the occurrences of events that involve human activities are subject to site and situational characteristics, and an understanding of event occurrences serves the basis for preparation or mitigation. Using data from Dallas, Texas, USA, we take the proposed approach to estimate the likelihood of traffic accidents based on binary (event or nonevent) space-time atoms of 100-m road segments and 1-h intervals. We choose 12 variables representing time, site characteristics, and situational conditions based on literature reviews to develop logistic regression and random forest models. The traffic accident data on even days were used for model construction and data on odd days for model testing. Both models result in comparable accuracy at 84.11% (logistic regression) and 85.42% (random forest) with significant differences in the spatial patterns of how site and situation correlate to traffic accidents. The difference signals the dynamic influence of site and situation characteristics on the event likelihood over time. The proposed approach shall be applicable to other point events on a network. [ABSTRACT FROM AUTHOR]