In accounting for phenomena present in preferential choice experiments, modern models assume a wide array of different mechanisms such as lateral inhibition, leakage, loss aversion, and saliency. These mechanisms create interesting predictions for the dynamics of the deliberation process as well as the aggregate behavior of preferential choice in a variety of contexts. However, the models that embody these different mechanisms are rarely subjected to rigorous quantitative tests of suitability by way of model fitting and evaluation. Recently, complex, stochastic models have been cast aside in favor of simpler approximations, which may or may not capture the data as well. In this article, we use a recently developed method to fit the four extant models of context effects to data from two experiments: one involving consumer goods stimuli, and another involving perceptual stimuli. Our third study investigates the relative merits of the mechanisms currently assumed by the extant models of context effects by testing every possible configuration of mechanism within one overarching model. Across all tasks, our results emphasize the importance of several mechanisms such as lateral inhibition, loss aversion, and pairwise attribute differences, as these mechanisms contribute positively to model performance. Together, our results highlight the notion that mathematical tractability, while certainly a convenient feature of any model, should neither be the primary impetus for model development nor the promoting or demotion of specific model mechanisms. Instead, model fit, balanced with model complexity, should be the greatest burden to bear for any theoretical account of empirical phenomena.