GRM Item Information Function

Computes the Item Information Function (IIF) for the Graded Response Model. The information function indicates how precisely an item measures ability at different theta levels.

Usage

ItemInformationFunc_GRM(theta, a, b)

Arguments

theta

Numeric. The ability parameter (theta).

a

Numeric. The slope (discrimination) parameter.

b

Numeric vector. The threshold (boundary) parameters.

Value

A numeric value representing the item information at the given ability level.

Details

For GRM, the Item Information Function is computed as: $$I(\theta) = a^2 \sum_{k=1}^{K-1} P_k^*(\theta) [1 - P_k^*(\theta)]$$

where \(P_k^*(\theta)\) is the cumulative probability of scoring in category \(k\) or above.

See also

plotICRF_gg

Examples

# Information at ability = 0 for a 5-category item
ItemInformationFunc_GRM(theta = 0, a = 1.5, b = c(-1, -0.5, 0.5, 1))
#> [1] 1.651687