Best model: hyperbolic model
$SV_t = reward_t \times \frac{1}{1 + k * effort_t}$
```r
> bic_summed
model aic bic n
1: hyperbolic 19017.25 19587.43 77 # lowest summed BIC across subjects
2: linear 19286.52 19856.69 77
3: sigmoid 19089.12 19944.38 77
4: parabolic 19416.46 19986.63 77
> dt1[, .(aic = mean(aic), bic = mean(bic)), by = .(model)] %>%
+ arrange(bic, aic) %>% data.table() # %>% fwrite("bic_mean.csv")
model aic bic
1: hyperbolic 246.9773 254.3822 # lowest mean BIC across subjects
2: linear 250.4742 257.8791
3: sigmoid 247.9107 259.0179
4: parabolic 252.1618 259.5666
```
![[summed_bic 1.jpg]]
```r
> dt2_avg
model N N_prop
1: linear 7 0.09090909 # best model for 7 subjects
2: hyperbolic 47 0.61038961 # best model for 47 subjects
3: sigmoid 10 0.12987013
4: parabolic 13 0.16883117
```
![[model_count 5.jpg]]