Expected a posteriori ability estimate

The posterior MEAN by Gauss-Hermite quadrature (Bock-Mislevy 1982). Three properties distinguish it from MAP: no optimisation at all (two weighted sums, so no convergence or multimodality problem – the reason adaptive testing prefers it), more shrinkage toward the prior mean since it is the minimum-MSE estimator, and a genuine posterior standard deviation rather than a curvature approximation. The node count is the only tuning parameter and is reported, because too few nodes silently biases the tails.

Usage

morie_psy_eap_theta(
  y,
  a = NULL,
  b = NULL,
  c = NULL,
  prior = c(0, 1),
  n_nodes = 61L
)

Arguments

y

binary responses.

a, b, c

item parameters; b required.

prior

c(mean, sd).

n_nodes

quadrature nodes.

Value

list: theta, se, posterior_sd, prior_mean, prior_sd, n_nodes, no_optimisation, n_items, method.

References

Bock and Mislevy (1982), Applied Psychological Measurement 6:431-444.

Examples

morie_psy_eap_theta(rep(1, 4), b = c(-1, -0.5, 0.5, 1))$theta
#> [1] 1.143879