Different models of categorization are often treated as competing accounts, but specific models are often used to understand individual differences, by estimating individual-level parameters. We develop an approach to understanding categorization that allows for individual differences both between and within models, using two prominent categorization models that make different theoretical assumptions: the Generalized Context Model (GCM) and General Recognition Theory (GRT). We develop a latent-mixture model for inferring whether an individual uses the GCM or GRT, while simultaneously allowing for the use of special-case simpler strategies. The GCM simple strategies involve attending to a single stimulus dimension, while the GRT simple strategies involve using unidimensional decision bounds. Our model also allows for simple contaminant strategies. We apply the model to four previously published categorization experiments, finding large and interpretable individual differences in the use of both models and specific strategies, depending on the nature of the stimuli and category structures.