Models | BIC/parameters | Experiment 1 (n = 24) | Experiment 2 (n = 17) | ||||
---|---|---|---|---|---|---|---|
Median | 25th percentile | 75th percentile | Median | 25th percentile | 75th percentile | ||
A, PE models | |||||||
ST | BIC | 95.1 | 84.0 | 114.8 | 103.1 | 96.1 | 108.8 |
ECunchosen(1): free | ECunchosen(1) | 7.51 | 4.69 | 10.61 | 11.05 | 6.44 | 13.16 |
α | 0.65 | 0.53 | 0.85 | 0.41 | 0.32 | 0.60 | |
β | 0.29 | 0.17 | 0.61 | 0.28 | 0.18 | 0.42 | |
ST | BIC | 91.3 | 81.8 | 109.7 | 99.7 | 95.0 | 106.3 |
ECunchosen(1) = ECchosen(1) | α | 0.66 | 0.57 | 0.87 | 0.53 | 0.38 | 0.65 |
β | 0.25 | 0.16 | 0.53 | 0.25 | 0.17 | 0.41 | |
HL | BIC | 83.3 | 64.2 | 106.5 | 80.7 | 67.9 | 97.0 |
ECunchosen(1): free | ECunchosen(1) | 0.75 | 0.67 | 0.87 | 0.75 | 0.71 | 0.96 |
α | 0.84 | 0.72 | 0.96 | 0.85 | 0.63 | 0.92 | |
β | 3.13 | 2.23 | 4.49 | 3.32 | 2.47 | 4.48 | |
HL | BIC | 78.5 | 59.2 | 101.4 | 81.9 | 63.3 | 93.4 |
ECunchosen(1) = ECchosen(1) | α | 0.80 | 0.71 | 0.96 | 0.87 | 0.64 | 0.97 |
β | 3.13 | 2.23 | 4.46 | 3.15 | 2.44 | 4.32 | |
IC | BIC | 135.2 | 128.6 | 138.0 | 130.9 | 126.8 | 134.9 |
ECunchosen(1): free | ECunchosen(1) | 0.70 | 0.49 | 1.11 | 0.90 | 0.41 | 1.29 |
α | 0.23 | 0.15 | 0.38 | 0.20 | 0.10 | 0.40 | |
β | 2.18 | −4.15 | 3.14 | 2.43 | −0.44 | 3.86 | |
IC | BIC | 130.7 | 123.9 | 134.0 | 126.2 | 124.5 | 130.8 |
ECunchosen(1) = ECchosen(1) | α | 0.29 | 0.18 | 0.46 | 0.20 | 0.12 | 0.32 |
β | 2.90 | 0.72 | 3.39 | 3.60 | 2.24 | 4.31 | |
ST-IC | BIC | 100.3 | 85.6 | 119.7 | 108.0 | 99.2 | 114.0 |
ECunchosen(1): free | ECunchosen(1) | 7.59 | 4.70 | 10.70 | 11.30 | 6.44 | 14.44 |
α | 0.65 | 0.53 | 0.84 | 0.40 | 0.32 | 0.60 | |
β | 0.29 | 0.17 | 0.60 | 0.28 | 0.18 | 0.40 | |
wincorrect | 0.67 | 0.00 | 6.96 | 0.00 | 0.00 | 0.00 | |
ST-IC | BIC | 96.4 | 83.4 | 114.6 | 104.1 | 98.3 | 111.5 |
ECunchosen(1) = ECchosen(1) | α | 0.67 | 0.57 | 0.86 | 0.53 | 0.38 | 0.65 |
β | 0.26 | 0.16 | 0.53 | 0.26 | 0.17 | 0.36 | |
wincorrect | 0.00 | 0.00 | 3.14 | 0.00 | 0.00 | 1.28 | |
HL-IC | BIC | 88.5 | 69.2 | 111.6 | 85.9 | 73.1 | 102.1 |
ECunchosen(1): free | ECunchosen(1) | 0.75 | 0.67 | 0.89 | 0.76 | 0.70 | 0.96 |
α | 0.83 | 0.72 | 0.93 | 0.85 | 0.64 | 0.92 | |
β | 3.38 | 2.18 | 4.40 | 3.16 | 2.36 | 4.58 | |
wincorrect | 0.00 | 0.00 | 0.14 | 0.00 | 0.00 | 0.08 | |
HL-IC | BIC | 83.7 | 64.2 | 106.5 | 84.3 | 68.5 | 98.6 |
ECunchosen(1) = ECchosen(1) | α | 0.80 | 0.71 | 0.96 | 0.87 | 0.64 | 0.97 |
β | 3.13 | 2.23 | 4.36 | 3.15 | 2.44 | 4.32 | |
wincorrect | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | |
B, PE-Rest models | |||||||
Rest | BIC | 132.3 | 129.0 | 134.0 | 131.0 | 125.5 | 132.1 |
α | 0.40 | 0.06 | 0.97 | 0.12 | 0.06 | 0.45 | |
β | 0.01 | −0.05 | 0.11 | 0.05 | −0.05 | 0.12 | |
HL-Rest | BIC | 88.7 | 69.2 | 103.8 | 92.8 | 73.6 | 109.0 |
αcost | 0.80 | 0.68 | 0.96 | 0.87 | 0.63 | 0.97 | |
αreward | 0.00 | 0.00 | 0.03 | 0.00 | 0.00 | 0.01 | |
β | −3.21 | −4.54 | −2.45 | −3.14 | −4.32 | −2.24 | |
wreward | −0.03 | −0.43 | 0.60 | 0.76 | −0.35 | 2.02 | |
C, pWSLS/PS models | |||||||
pWSLS-HL | BIC | 92.9 | 79.0 | 110.8 | 97.1 | 91.1 | 109.4 |
p | 0.19 | 0.14 | 0.27 | 0.21 | 0.18 | 0.27 | |
pWSLS-IC | BIC | 111.1 | 88.6 | 124.7 | 100.9 | 92.7 | 110.8 |
p | 0.76 | 0.67 | 0.85 | 0.80 | 0.76 | 0.83 | |
PS-HL | BIC | 69.4 | 57.8 | 87.4 | 70.1 | 54.6 | 90.2 |
a | 0.95 | 0.91 | 0.98 | 0.97 | 0.91 | 0.98 | |
b | 0.47 | 0.30 | 0.58 | 0.48 | 0.46 | 0.58 | |
PS-IC | BIC | 111.1 | 88.6 | 124.7 | 100.9 | 92.7 | 110.8 |
a | 0.76 | 0.67 | 0.85 | 0.80 | 0.76 | 0.83 | |
b | 0.50 | 0.41 | 0.55 | 0.66 | 0.50 | 0.77 |
This table shows the median, 25th, and 75th percentiles of BIC scores and best-fit parameter estimates for 10 variants of PE models (5 assumptions on ActualCost [Solve-Time (SV), High-Low (HL), Incorrect-Correct (IC), ST-IC, and HL-IC] × 2 assumptions on ECunchosen(1) [free parameter or equal to ECchosen(1)]), two types of additionally considered PE models (Rest and HL-Rest models), and pWSLS and PS models. ECunchosen, the expected cost for the unchosen option; ECchosen, the expected cost for the chosen option; α, learning rate; β, inverse temperature; wincorrect, weighting parameter; αcost, the learning rate for cost; αreward, the learning rate for reward; wreward, weighting parameter; p, probability to select the different and same option after Win and Lose, respectively; a, probability to select the same option after Win; b, probability to select the same option after Lose.