Categorical decisions: I started my academic career working to improve formal models of categorical decisions, the main conclusions from this work being (a) the ratio rule (aka Luce choice axiom) is an inadequate model of categorical decisions (e.g. Wills et al., 2000), and (b) there is a level of representation intermediate betweem stimulus representations and category-label representations (Wills et al., 2006).
Approaches to model comparison: Since around 2008, I’ve been thinking a lot about the problem of formal model comparison, leading to a fairly strong statement of the problem (Wills & Pothos, 2012), followed by some proactive attempts to begin to solve the problem (Wills et al., 2017), including a range of open-source software.
The CAL model: One of the unexpected side benefits of this thinking about model comparison is that it brought me into contact with René Schlegelmilch, who started developing the CAL model of category learning during as a visiting Ph.D. student in my lab in 2017. CAL is a fascinating and sophisticated new model of category learning, which you can read about in preprint form below (Schlegelmilch et al., 2020).
Schlegelmilch, R., Wills, A.J. & von Helversen, B. (2020). A Cognitive Category-Learning Model of Rule Abstraction, Attention Learning, and Contextual Modulation. preprint.
Wills, A.J., O’Connell, G., Edmunds, C.E.R., & Inkster, A.B. (2017). Progress in modeling through distributed collaboration: Concepts, tools, and category-learning examples. Psychology of Learning and Motivation, 66, 79-115.
Wills, A.J. (2013). Models of categorization. In D. Reisberg (Ed.). Oxford Handbook of Cognitive Psychology (pp. 346-357). Oxford: Oxford University Press.
Wills, A.J., & Pothos, E.M. (2012). On the adequacy of current empirical evaluations of formal models of categorization. Psychological Bulletin, 138, 102-125.
Pothos, E.M., & Wills, A.J. (2011). Formal approaches in categorization. Cambridge University Press.
Wills, A.J., Noury, M., Moberly, M.J., & Newport, M. (2006). Formation of category representations. Memory and Cognition, 34, 17-27.
Wills, A.J., Reimers, S., Stewart, N., & McLaren, I.P.L. (2000). Tests of the ratio rule in categorization. Quarterly Journal of Experimental Psychology, 53A, 983-1011.
Jones, F.W., Wills, A.J., & McLaren, I.P.L. (1998). Perceptual categorization: connectionist modelling and decision rules. Quarterly Journal of Experimental Psychology, 51B, 33-58.
Wills, A.J., & McLaren, I.P.L. (1997). Generalization in human category learning: A connectionist explanation of differences in gradient after discriminative and non-discriminative training. Quarterly Journal of Experimental Psychology, 50A, 607-630.