alt_delta() returning similar parameter estimates for all participants

[Matt-A-Johnson]

When using alt_delta() in r I keep getting virtually the same parameter estimates for each participant. I thought alt_delta() should return separate parameter estimates for each participant? I have run the same data through other Rescorla Wagner (RW) models (outside of hBayesDM), and I can see that the values are different for each participant. It is probably me being dim, but why might alt_delta() be returning similar estimates for each participant? Specifically, alt_delta() returns alpha approx. 0.5 for each participant. Any help/advice on this is greatly appreciated- thanks.

Pilot_LM_Data.csv

#Create data frame to house necessary variables:
data_STO <- read.csv("Pilot_LM_Data.csv") %>%
  filter(blockname == "STO") %>%
  select(subjID = subject,
          choice = response,
          outcome = feedback,
          bluePunish = feedback,
          orangePunish = feedback) %>%
  mutate(
    choice = ifelse(choice == 18, 1, 2),
    outcome = ifelse(outcome == 1, 0, 1),
    bluePunish = ifelse(outcome == 0, -1, 1),
    orangePunish = ifelse(outcome == 0, -1, 1)
  )

#Fit learning model:
LR_STO <- alt_delta(
  data = data_STO,
  niter = 4000,
  nwarmup = 1000,
  nchain = 4,
  ncore = 4,
  nthin = 1,
  inits = "vb",
  indPars = "mean",
  modelRegressor = FALSE,
  vb = FALSE,
  inc_postpred = FALSE,
  adapt_delta = 0.95,
  stepsize = 1,
  max_treedepth = 10
)

#Print parameter estimates for each participant:
LR_STO$allIndPars

[lehlsy0904]

Hello,

Thanks for providing all the details. The issue you’re experiencing with alt_delta() returning similar parameter estimates for each participant could be due to shrinkage effect, a common feature in hierarchical Bayesian modeling. In hierarchical models, individual parameter estimates are “pulled” toward the group-level mean, especially when there is limited variability in the data or when participant-level data is sparse. This shrinkage is a useful property for stabilizing estimates but can sometimes mask individual differences if the effect is too strong.

To further investigate, you might try fitting other models in hBayesDM (e.g., bandit2arm_delta, prl_fictitious_rp), which are also designed for two-armed bandit tasks. Testing these alternative models can help you determine whether similar results occur across different models or are specific to alt_delta().

Please feel free to reach out if you have additional questions or need further assistance.

Best,
Eunhwi