- [[20211031_184032 extra analyses for linear model - multiple k ONE b]] # BIC Summed ```r > bic_summed study model aic bic 1: 1 linear_manyk_oneb 8676.439 9774.540 2: 1 linear_manyk_manyb 8436.461 9900.596 3: 1 parabolic_manyk_manyb 9448.472 10912.607 4: 1 hyperbolic_manyk_oneb 10479.988 11578.089 5: 1 parabolic_manyk_oneb 10726.708 11824.809 6: 1 hyperbolic_manyk_manyb 10546.336 12010.470 7: 2 linear_manyk_manyb 12844.345 14753.506 8: 2 hyperbolic_manyk_oneb 14578.280 15851.054 9: 2 parabolic_manyk_manyb 14159.389 16068.550 10: 2 hyperbolic_manyk_manyb 14848.126 16757.286 11: 2 linear_manyk_oneb 16580.115 17852.889 12: 2 parabolic_manyk_oneb 20382.571 21655.344 ``` Mean ```r study model aic bic 1: 1 linear_manyk_oneb 70.54015 79.46780 2: 1 linear_manyk_manyb 68.58912 80.49265 3: 1 parabolic_manyk_manyb 76.81685 88.72038 4: 1 hyperbolic_manyk_oneb 85.20315 94.13080 5: 1 parabolic_manyk_oneb 87.20901 96.13666 6: 1 hyperbolic_manyk_manyb 85.74257 97.64610 7: 2 linear_manyk_manyb 136.64197 156.95219 8: 2 hyperbolic_manyk_oneb 155.08808 168.62823 9: 2 parabolic_manyk_manyb 150.63180 170.94202 10: 2 hyperbolic_manyk_manyb 157.95878 178.26900 11: 2 linear_manyk_oneb 176.38420 189.92435 12: 2 parabolic_manyk_oneb 216.83586 230.37600 ``` Median ```r study model aic bic 1: 1 linear_manyk_manyb 61.17224 72.96728 2: 1 linear_manyk_oneb 67.30640 76.33830 3: 1 parabolic_manyk_manyb 80.68016 91.96916 4: 1 parabolic_manyk_oneb 88.40368 97.35247 5: 1 hyperbolic_manyk_oneb 91.90632 100.83653 6: 1 hyperbolic_manyk_manyb 92.52323 104.43016 7: 2 linear_manyk_manyb 143.69367 164.16349 8: 2 parabolic_manyk_manyb 159.86827 180.35151 9: 2 hyperbolic_manyk_oneb 174.00188 187.63041 10: 2 linear_manyk_oneb 184.53638 197.62838 11: 2 hyperbolic_manyk_manyb 181.81237 202.30897 12: 2 parabolic_manyk_oneb 236.59336 250.12088 ``` When all subjects are included in the analyses, the linear model was the best-fitting model. Though depending on which metric we use, the model with multiple b or one b parameter was the best model. In study 2, 43 subjects fitted better with hyperbolic models and 43 fitted better with linear models (so 50-50!). ![[model_count 3.jpg]] ```r study model_spec N N_prop 1: 1 Linear 71 0.57723577 2: 1 Hyperbolic 26 0.21138211 3: 1 Parabolic 26 0.21138211 4: 2 Hyperbolic 43 0.45744681 5: 2 Linear 43 0.45744681 6: 2 Parabolic 8 0.08510638 ``` # k ~ target ![[k 4.jpg]] Study 1 ```r > summaryh(mk1) term results 1: (Intercept) b = 0.08, SE = 0.02, t(195) = 4.80, p < .001, r = 0.33 2: targetCharity b = 0.04, SE = 0.02, t(122) = 2.12, p = .036, r = 0.19 ``` Study 2 ```r F(2, 186) = 14.04, p < .001 # self as reference > summaryh(mk1) term results 1: (Intercept) b = 0.07, SE = 0.02, t(217) = 3.11, p = .002, r = 0.21 2: targetCharity b = 0.06, SE = 0.03, t(186) = 2.21, p = .028, r = 0.16 3: targetIntragroup stranger b = 0.13, SE = 0.03, t(186) = 5.28, p < .001, r = 0.36 # charity as reference term results 1: (Intercept) b = 0.13, SE = 0.02, t(217) = 5.58, p < .001, r = 0.35 2: targetSelf b = −0.06, SE = 0.03, t(186) = −2.21, p = .028, r = 0.16 3: targetIntragroup stranger b = 0.08, SE = 0.03, t(186) = 3.07, p = .003, r = 0.22 ``` # b ~ target ![[b 4.jpg]] Study 1 ```r term results 1: (Intercept) b = 1.37, SE = 0.07, t(219) = 19.71, p < .001, r = 0.80 2: targetCharity b = −0.03, SE = 0.08, t(122) = −0.32, p = .753, r = 0.03 ``` Study 2 ```r F(2, 186) = 19.75, p < .001 # self as reference term results 1: (Intercept) b = 1.13, SE = 0.06, t(267) = 19.62, p < .001, r = 0.77 2: targetCharity b = −0.26, SE = 0.07, t(186) = −3.48, p < .001, r = 0.25 3: targetIntragroup stranger b = −0.47, SE = 0.07, t(186) = −6.27, p < .001, r = 0.42 # charity as reference term results 1: (Intercept) b = 0.86, SE = 0.06, t(267) = 15.07, p < .001, r = 0.68 2: targetSelf b = 0.26, SE = 0.07, t(186) = 3.48, p < .001, r = 0.25 3: targetIntragroup stranger b = −0.21, SE = 0.07, t(186) = −2.79, p = .006, r = 0.20 ``` # winning model: separate k, separate b $sv = reward \times (1 - k \times effort)$ Mean SV across participants. ![[linear_function 8.jpg]]