Parameter Update Functions

In meow: Unified Framework for Computer Adaptive Testing Simulations

knitr::opts_chunk$set(collapse = TRUE, comment = "#>")
library(meow)

Parameter update functions re-estimate person and item parameters from the responses administered so far. They are the estimation engine of a meow simulation and can form the bulk of your runtime. For the full module contract, see vignette("extending-meow").

Function signature

Every parameter update function has the signature

update_fun <- function(pers, item, R, admin, ...) {
  # ... re-estimate parameters ...
  list(pers = updated_pers, item = updated_item)
}

It receives the current person and item parameter estimates (pers, item), the full response matrix R, and the non-negative integer valued administration matrix admin. Parameter update functions return a list with the updated pers and item data frames. The responses to administered items are obtained from the matrix state:

idx    <- which(admin != 0, arr.ind = TRUE)
persons <- unique(idx[, 1])
items <- unique(idx[, 2])
resp   <- R[idx]

or, equivalently, as a long data frame with meow_long(R, admin).

Bundled updaters

Maximum likelihood ability estimation

update_theta_mle() treats item parameters as fixed and finds each respondent's 2PL maximum likelihood ability estimate, constrained to $[-4, 4]$. The log-likelihood is fully vectorized over the administered responses:

loglik <- function(theta) {
  p <- stats::plogis(item$a[item_j] * (theta[person] - item$b[item_j]))
  sum(resp * log(p) + (1 - resp) * log(1 - p))
}
est <- stats::optim(pers$theta, loglik, lower = -4, upper = 4,
                    method = "L-BFGS-B", control = list(fnscale = -1))

Elo-style updates (Maths Garden)

update_maths_garden() updates both abilities and difficulties with the on-the-fly Elo rule of Klinkenberg, Straatemeier, and van der Maas (2011):

$$\hat\theta_j = \theta_j + K_\theta \sum_i (S_{ij} - E(S_{ij})), \qquad \hat b_i = b_i + K_b \sum_j (E(S_{ij}) - S_{ij}).$$

See vignette("maths-garden-update").

Paired Elo updates (Prowise Learn)

update_prowise_learn() updates abilities with the same rule, but updates item difficulties through paired comparisons of consecutively administered items, which controls rating drift (Vermeiren et al., 2025). See vignette("prowise-learn-update").

Best practices

1. Return list(pers, item) with both objects as both data frames, even if one is unchanged.
2. Bound estimates to a sensible range to avoid divergence.
3. Vectorize over the administered responses (tapply(), matrix indexing) rather than looping over respondents or items.
4. Respect administration order when it matters: The best method is to use values from the admin matrix, but meow_long() returns responses ordered by respondent and then by administration order.

meow documentation built on July 6, 2026, 5:11 p.m.