grm_iif: Item Information Function for GRM

In exametrika: Test Data Engineering

Item Information Function for GRM

Description

Calculates the value of the Item Information Function for the Graded Response Model.

Usage

grm_iif(theta, a, b)

Arguments

theta	Latent trait value of the subject
a	Discrimination parameter of IRF
b	Vector of difficulty parameters (thresholds) of IRF

Details

The information is Samejima's (1969) item information for the GRM,

I(\theta) = \sum_{k=1}^{K} \frac{[P_k'(\theta)]^2}{P_k(\theta)},

where P_k(\theta) = P_{k-1}^*(\theta) - P_k^*(\theta) is the category response probability, P_k^*(\theta) is the cumulative (boundary) probability with P_0^* = 1 and P_K^* = 0, and P_k^{*\prime}(\theta) = a P_k^*(\theta) [1 - P_k^*(\theta)]. The logistic metric of the estimation routine is used as is (no 1.702 scaling constant), so the information is consistent with the parameters returned by GRM and with the posterior standard deviations (PSD).

Value

Value of the Item Information Function

Examples

## Not run: 
# Example for an item with 3 categories
a <- 1.5
b <- c(-1.0, 1.0)
thetas <- seq(-3, 3, by = 0.1)
info <- sapply(thetas, function(t) grm_iif(t, a, b))
plot(thetas, info, type = "l", xlab = "Theta", ylab = "Information")

## End(Not run)

exametrika documentation built on Aug. 20, 2026, 5:08 p.m.