Statistical models as cognitive models of individual differences in reasoning

There are individual differences in reasoning which go beyond dimensions of ability. Valid models of cognition must take these differences into account, otherwise they characterise group mean phenomena which explain nobody. The gap is closing between formal cognitive models, which are designed from the ground up to explain cognitive phenomena, and statistical models, which traditionally concern the more modest task of modelling relationships in data. This paper critically reviews three illustrative statistical models of individual differences in reasoning which embed some notion of cognitive process. Although the models are each developed in different frameworks, it is shown that they are more similar than would first appear. The cognitive meaning of elements in the example models is explored and some sketches are developed for future directions of research.