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Chained Onsets

Source: vignettes/chained_onset.Rmd
chained_onset.Rmd

This vignette shows how to define staged processing with after(). Here accumulator C starts only after accumulator B has finished.

## 
## Attaching package: 'AccumulatR'
## The following object is masked from 'package:stats':
## 
##     simulate

Define the model A is directly observed. B is latent. C is observed and starts only after B has finished.

model <- race_spec() |>
  add_accumulator("A", "lognormal") |>
  add_accumulator("B", "lognormal") |>
  add_accumulator("C", "lognormal", onset = after("B")) |>
  add_outcome("A", "A") |>
  add_outcome("C", "C") |>
  finalize_model()

true_params <- c(
  A.m = log(0.28),
  A.s = 0.14,
  B.m = log(0.1),
  B.s = 0.1,
  C.m = log(0.15),
  C.s = 0.1
)

Simulate data Each trial contributes an observed response label and response time.

set.seed(123456)

n_trials <- 2000
params_df <- build_param_matrix(model, true_params, n_trials = n_trials)

sim <- simulate(model, params_df)

data_df <- data.frame(
  trial = sim$trial,
  R = factor(sim$R),
  rt = sim$rt,
  stringsAsFactors = FALSE
)

table(data_df$R)
## 
##    A    C 
##  446 1554

Estimate parameters with optim() We estimate A.m, A.s, B.m, B.s, C.m, and C.s. The spread parameters are optimized on the log scale.

prepared <- prepare_data(model, data_df)
ctx <- make_context(model)

neg_loglik <- function(theta) {
  est <- true_params
  est[c("A.m", "A.s", "B.m", "B.s", "C.m", "C.s")] <- theta[c("A.m", "A.s", "B.m", "B.s", "C.m", "C.s")]
  est[c("A.s", "B.s", "C.s")] <- exp(est[c("A.s", "B.s", "C.s")])
  params_df <- build_param_matrix(
    model,
    est,
    trial_df = prepared
  )
  ll <- log_likelihood(ctx, prepared, params_df)
  -as.numeric(ll)
}

start <- c(
  A.m = log(0.22),
  A.s = log(0.10),
  B.m = log(0.28),
  B.s = log(0.10),
  C.m = log(0.28),
  C.s = log(0.10)
)

set.seed(123456)
fit <- optim(start, neg_loglik, method = "Nelder-Mead")
fit_params <- fit$par
fit_params[c("A.s", "B.s", "C.s")] <- exp(fit_params[c("A.s", "B.s", "C.s")])
target <- true_params[c("A.m", "A.s", "B.m", "B.s", "C.m", "C.s")]

data.frame(
  true = target,
  recovered = fit_params,
  miss = abs(target - fit_params)
)
##          true   recovered        miss
## A.m -1.272966 -1.25003011 0.022935562
## A.s  0.140000  0.09451568 0.045484321
## B.m -2.302585 -2.84037595 0.537790857
## B.s  0.100000  0.02842790 0.071572096
## C.m -1.897120 -1.64098410 0.256135882
## C.s  0.100000  0.10959761 0.009597612

Use chained onsets when the model requires a staged dependency between processes. We do note that these models can suffer from weak identifiability. So use with care!