Comparing likelihood-based and likelihood-free approaches to fitting and comparing models of intertemporal choice

Machine learning methods have recently begun to be used for fitting and comparing cognitive models, yet they have mainly focused on methods for dealing with models that lack tractable likelihoods. Evaluating how these approaches compare to traditional likelihood-based methods is critical to understanding the utility of machine learning for modeling and determining what role it might play in the development of new models and theories. In this paper, we systematically benchmark neural network approaches against likelihood-based approaches to model fitting and comparison, focusing on intertemporal choice modeling as an illustrative application. By applying each approach to intertemporal choice data from participants with substance use problems, we show that there is a high degree of convergence between neural network and Bayesian methods when it comes to making inferences about latent processes and real outcomes. For model comparison, however, classification networks significantly outperformed likelihood-based metrics. Next, we extended neural networks in two ways, using recurrent layers to allow them to fit data with variable stimuli and numbers of trials, and using dropout layers to allow for posterior sampling. We ultimately suggest that neural networks are better suited to fast parameter estimation, posterior sampling, large data sets, and model comparison, while hierarchical Bayesian methods should be preferred for flexible applications across different experimental designs.