Log-likelihood surface of an item's discrimination and difficulty

The log-likelihood of the responses of people with known abilities to one item, for every combination of discrimination and difficulty on a grid, under the three-parameter logistic model with a known lower asymptote (the two-parameter logistic model when c = 0) and \(D = 1\).

Usage

loglik_surface(
  responses,
  theta,
  a = seq(-3, 3, by = 0.1),
  b = seq(-3, 3, by = 0.1),
  c = 0
)

Arguments

responses

Ones and zeros, the responses of the people.

theta

Abilities of the people.

a

Grid of discriminations.

b

Grid of difficulties.

c

Lower asymptote assumed for the item.

Value

A matrix with one row for each value of a and one column for each value of b, which keeps the two grids as its attributes a and b.

Examples

set.seed(1)
theta <- seq(-3, 3, length.out = 50)
surface <- loglik_surface(simulate_responses(theta, a = 1, b = -0.5), theta)
surface_maximum(surface)
#> $a
#> [1] 1.2
#> 
#> $b
#> [1] -1.3
#> 
#> $loglik
#> [1] -18.46392
#>