In this paper, we propose a generalized linear model for video packet loss visibility that is applicable to different group-of-picture structures. We develop the model using three subjective experiment data sets that span various encoding standards (H.264 and MPEG-2), group-of-picture structures, and decoder error concealment choices. We consider factors not only within a packet, but also in its vicinity, to account for possible temporal and spatial masking effects. We discover that the factors of scene cuts, camera motion, and reference distance are highly significant to the packet loss visibility. We apply our visibility model to packet prioritization for a video stream; when the network gets congested at an intermediate router, the router is able to decide which packets to drop such that visual quality of the video is minimally impacted. To show the effectiveness of our visibility model and its corresponding packet prioritization method, experiments are done to compare our perceptual-quality-based packet prioritization approach with existing Drop-Tail and Hint-Track-inspired cumulative-MSE-based prioritization methods. The result shows that our prioritization method produces videos of higher perceptual quality for different network conditions and group-of-picture structures. Our model was developed using data from high encoding-rate videos, and designed for high-quality video transported over a mostly reliable network; however, the experiments show the model is applicable to different encoding rates.