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Efficient selection between hierarchical cognitive models: cross-validation with Variational Bayes

Mr. Hung Dao
UNSW Sydney ~ School of Economics
Dr. Robert Kohn
University of New South Wales ~ Australian School of Business
Dr. Scott Brown
University of Newcastle ~ School of Psychology
Guy Hawkins
University of Newcastle ~ School of Psychological Sciences
Dr. Minh-Ngoc Tran
University of Sydney Business School ~ Discipline of Business Analytics
Dr. David Gunawan
University of Wollongong, Australia ~ School of Mathematics and Applied Statistics

Model comparison is the cornerstone of theoretical progress in psychological research. Common practice overwhelmingly relies on tools that evaluate competing models by balancing in-sample descriptive adequacy against model flexibility, with modern approaches advocating the use of marginal likelihood for hierarchical cognitive models. Cross-validation is another popular approach but its implementation has remained out of reach for cognitive models evaluated in a Bayesian hierarchical framework, with the major hurdle being prohibitive computational cost. To address this issue, we develop novel algorithms that make Variational Bayes (VB) inference for hierarchical models feasible and computationally efficient for complex cognitive models of substantive theoretical interest. It is well known that VB produces good estimates of the first moments of the parameters which gives good predictive densities estimates. We thus develop a novel VB algorithm with Bayesian prediction as a tool to perform model comparison by cross-validation, which we refer to as CVVB. In particular, the CVVB can be used as a model screening device that quickly identifies bad models. We demonstrate the utility of CVVB by revisiting a classic question in decision making research: what latent components of processing drive the ubiquitous speed-accuracy trade-off? We demonstrate that CVVB strongly agrees with model comparison via marginal likelihood yet achieves the outcome in much less time. Our approach brings cross-validation within reach of theoretically important psychological models, and makes it feasible to compare much larger families of hierarchically specified cognitive models than has previously been possible.



Model Selection
Variational Bayes
Bayesian Inference
Cognitive Models

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Cite this as:

Dao, V., Kohn, R., Brown, S., Hawkins, G., Tran, M.-N., & Gunawan, D. (2021, July). Efficient selection between hierarchical cognitive models: cross-validation with Variational Bayes. Paper presented at Virtual MathPsych/ICCM 2021. Via