Fit the expected-gain model

Marginal maximum likelihood on a theta grid, in two stages: (1) the attempt-1 ability distribution of repeaters, N(mu1, s1); (2) growth `theta2 = theta1 + X beta + N(0, sigma_growth)` from attempt-1 responses and attempt-2 responses to **new items only**. Because exposed items never enter the growth model, preknowledge cannot inflate the expected gain, and conditioning on the full attempt-1 likelihood handles regression to the mean.

Usage

rt_fit(
  data,
  growth = ~log(days_between) + remediation,
  grid = seq(-5, 5, by = 0.2)
)

Arguments

data

An `rt_data` (or `rt_sim`) object.

growth

One-sided formula for mean growth, evaluated in `data$persons`.

grid

Theta grid.

Value

An `rt_fit` object.

Examples

sim <- rt_simulate(n_persons = 200, form_exposed = 20, form_new = 10, seed = 1)
fit <- rt_fit(sim)
fit    # growth coefficients: intercept, log(days_between), remediation
#> <rt_fit> expected-gain model, 200 repeaters
#> attempt-1 ability: N(-0.499, 0.701^2)
#> growth coefficients:
#>                   estimate    se
#> (Intercept)          0.112 0.460
#> log(days_between)    0.027 0.090
#> remediation          0.714 0.129
#> growth SD: 0.299 | log-RT residual SD: 0.501