Aggregation of rigid colloidal particles leads to fractal-like structures that are characterized by a fractal dimension d(f) which is a key parameter for describing aggregation processes. This is particularly true in shear aggregation where d(f) strongly influences aggregation kinetics. Direct measurement of d(f) in the early stages of shear aggregation is however difficult, as the aggregates are small and few in number. An alternative method for determining d(f) is to use an aggregation model that when fitted to the time evolution of the cluster mass distribution allows for estimating d(f). Here, we explore three such models, two of which are based on an effective collision sphere and one which directly incorporates the permeable structure of the aggregates, and we apply them for interpreting the initial aggregate growth measured experimentally in a turbulent stirred tank reactor. For the latter, three polystyrene latexes were used that differed only in the size of the primary particles (d(p) = 420, 600, and 810 nm). It was found that all three models describe initial aggregation kinetics reasonably well using, however, substantially different values for 4 To discriminate among the models, we therefore also studied the regrowth of preformed aggregates where d(f) was experimentally accessible. It was found that only the model that directly incorporates the permeable structure of the aggregates is able to predict correctly this second type of experiments. Applying this model to the initial aggregation kinetics, we conclude that the actual initial fractal dimension is d(f) = 2.07 +/- 0.04 as found from this model.