Journal: eLife
Article Title: Time preferences are reliable across time-horizons and verbal versus experiential tasks
doi: 10.7554/eLife.39656
Figure Lengend Snippet: BHM model fits (x-axis) vs. Matlab individual data fits (y-axis) across tasks against the unity line. Since the estimation procedure was identical for all MLE fits (Matlab code is available on github repository), we describe it using the softmax-hyperbolic model as an example. This is a two-parameter model to estimate choice behavior, that is, it transforms the stimulus on each trial (inputs to the model include rewards and delays for sooner and later options) into a probability distribution about the subject’s choice. For example, if for a given set of parameters, the model predicts that trial one will result in 80% chance of the subject choosing later option, and the subject, in fact, chose the later, the trial would be assigned a likelihood of 0.8 (if the subject chose sooner, the trial would have a likelihood of 0.2). Finally, we perform a leave-one-out cross-validation for each subject-task to avoid overfitting. We leave one trial out and use the rest of the trials in the experimental task to predict this trial. We repeat this procedure for each trial. Instead of getting point estimates (or distributions of parameter values through cross-validation as we did) one can use a Bayesian hierarchical model (BHM, estimation details in Materials and methods) to find full posterior distributions. It allows for both pooling data across subjects and recognizing individual differences. The fits from BHM model are almost identical to the individual fits done for each experimental task separately using softmax-hyperbolic model and ‘fmincon’ function in Matlab. The exceptions are very patient subjects that almost exclusively picked the later option. For these subjects, the MLE fits can produce discount factors < e - 10 , but the prior in the BHM model constrains these to be around e - 8 . Furthermore, the rank correlation values for MLE fits correspond to the BHM ones both in magnitude and significance. Rank correlations obtained from individual level MLE fits for top three models by BIC: (NV vs. SV) Spearman r = 0.52, 0.68, 0.38 for hyperbolic utility with matching rule, hyperbolic utility with softmax and exponential utility with softmax models, respectively; (SV vs. LV) Spearman r = 0.46, 0.49, 0.5, all p < 0.01 .
Article Snippet: We validated that our results were not sensitive to the model fitting methods used; the means of BHM posteriors of the individual discount-factors for each task are almost identical to the individual fits done for each experimental task separately using maximum likelihood estimation through fmincon in Matlab ( , ).
Techniques: Biomarker Discovery
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