# `include == 1` subjects ## fitted params ~ simulated params We performed parameter recovery to check model fit. For each participant, we simulated data using the fitted parameters (100 trials per unique effort-reward pair for each target). We then fitted the model using the maximum likelihood approach described in the main analysis to recover the parameters. The results are shown in the two figures below. There is agreement between the fitted and simulated parameter values (Fig XXX). Crucially, the model-predicted choices also correlated highly with observed choices (Fig. XXX). ```r # correlation between fitted parameter and simulated parameter Study Parameter term results 1: 1 b Simulated_parameter b = 0.49, SE = 0.14, t(49) = 3.44, p = .001, r = 0.44 2: 2 b Simulated_parameter b = 0.39, SE = 0.16, t(44) = 2.47, p = .018, r = 0.35 3: 1 k Simulated_parameter b = 0.82, SE = 0.10, t(49) = 8.18, p < .001, r = 0.76 4: 2 k Simulated_parameter b = 0.94, SE = 0.14, t(44) = 6.54, p < .001, r = 0.70 ``` ![[fitted-simulated-params-include1.jpg]] Figure XXX. Parameter recovery for the linear discounting model with separate k and b parameters for each target. Each dot is one participant. Dots that fall on the diagonal indicate excellent model fit: The simulated parameter values are identical to the fitted parameter values. ## Observed choice ~ model-predicted choice ```r # correlation between observed choice and predicted choice Study Target term results 1: 1 Charity predicted_choice b = 1.02, SE = 0.03, t(49) = 36.25, p < .001, r = 0.98 2: 1 Self predicted_choice b = 1.00, SE = 0.03, t(49) = 37.12, p < .001, r = 0.98 3: 2 Charity predicted_choice b = 1.09, SE = 0.04, t(44) = 30.55, p < .001, r = 0.98 4: 2 Intragroup stranger predicted_choice b = 1.16, SE = 0.05, t(44) = 21.76, p < .001, r = 0.96 5: 2 Self predicted_choice b = 0.98, SE = 0.02, t(44) = 41.81, p < .001, r = 0.99 ``` ![[choice-observed-predicted-include1 1.jpg]] Figure XXX. Model fit for the linear discounting model with separate k and b parameters for each target. Each dot is one participant. Dots that fall on the diagonal indicate excellent model fit: The model-predicted choices are identical to the observed choices. # all subjects ## fitted params ~ simulated params All subjects ```r # correlation between fitted parameter and simulated parameter Study Parameter term results 1: 1 b Simulated_parameter b = 0.51, SE = 0.09, t(121) = 5.58, p < .001, r = 0.45 2: 2 b Simulated_parameter b = 0.20, SE = 0.10, t(92) = 1.92, p = .058, r = 0.20 3: 1 k Simulated_parameter b = 0.98, SE = 0.06, t(121) = 15.31, p < .001, r = 0.81 4: 2 k Simulated_parameter b = 1.01, SE = 0.07, t(92) = 14.30, p < .001, r = 0.83 ``` ![[fitted-simulated-params-allsubjects.jpg]] ## Observed choice ~ model-predicted choice ```r # correlation between observed choice and predicted choice Study Target term results 1: 1 Self predicted_choice b = 1.03, SE = 0.01, t(121) = 84.66, p < .001, r = 0.99 2: 1 Charity predicted_choice b = 1.04, SE = 0.01, t(121) = 95.11, p < .001, r = 0.99 3: 2 Self predicted_choice b = 0.89, SE = 0.05, t(92) = 19.08, p < .001, r = 0.89 4: 2 Charity predicted_choice b = 1.06, SE = 0.03, t(92) = 39.04, p < .001, r = 0.97 5: 2 Intragroup stranger predicted_choice b = 1.13, SE = 0.02, t(92) = 53.52, p < .001, r = 0.98 ``` ![[choice-observed-predicted-allsubjects.jpg]]