Normalization in positron emission tomography (PET) is the process of ensuring that all lines of response joining detectors in coincidence have the same effective sensitivity. In three-dimensional (3D) PET, normalization is complicated by the presence of a large proportion of scattered coincidences, and by the fact that cameras operating in 3D mode encounter a very wide range of count-rates. In this work a component-based normalization model is presented which separates the normalization of true and scattered coincidences and accounts for variations in normalization effects with count-rate. The effects of the individual components in the model on reconstructed images are investigated, and it is shown that only a subset of these components has a significant effect on reconstructed image quality.