Information surface of a two-dimensional dichotomous item

The item information at each point: the squared slope of the response surface of prob_mirt(), in the direction in which it rises fastest, divided by $P (1 - P)$, $$I(\theta_1, \theta_2) = \frac{(\partial P / \partial \theta_1)^2 + (\partial P / \partial \theta_2)^2}{P (1 - P)}.$$ For the compensatory model this is the information of the four-parameter logistic model (Magis, 2013) along the item vector, $D^2 A^2 (P - c)^2 (d - P)^2 / ((d - c)^2 P (1 - P))$, with $A = \sqrt{a_1^2 + a_2^2}$. Where $P$ is exactly 0 or 1, or $c = d$, the surface is flat and the information is 0.

Usage

info_mirt(
  theta1,
  theta2,
  a = c(1, 1),
  b = c(0, 0),
  c = 0,
  d = 1,
  D = 1.702,
  compensatory = TRUE
)

Arguments

theta1, theta2: Numeric vectors of abilities on the two dimensions.
a: Discriminations on the two dimensions.
b: Locations on the two dimensions.
c: Lower asymptote.
d: Upper asymptote.
D: Scaling constant.
compensatory: TRUE for the compensatory model, FALSE for the non-compensatory one.

Value

A matrix with one row for each value of theta1 and one column for each value of theta2.

References

Magis, D. (2013). A note on the item information function of the four-parameter logistic model. Applied Psychological Measurement, 37(4), 304-315.

Examples

theta <- seq(-4, 4, length.out = 5)
info_mirt(theta, theta)
#>              [,1]         [,2]        [,3]         [,4]         [,5]
#> [1,] 7.072849e-06 0.0002127659 0.006387238 0.1803882447 1.448402e+00
#> [2,] 2.127659e-04 0.0063872380 0.180388245 1.4484020000 1.803882e-01
#> [3,] 6.387238e-03 0.1803882447 1.448402000 0.1803882447 6.387238e-03
#> [4,] 1.803882e-01 1.4484020000 0.180388245 0.0063872380 2.127659e-04
#> [5,] 1.448402e+00 0.1803882447 0.006387238 0.0002127659 7.072849e-06