Item Response Theory (IRT)

In exametrika: Test Data Engineering

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 7,
  fig.height = 5,
  out.width = "100%"
)

library(exametrika)

IRT for Binary Data

The IRT() function estimates item parameters using logistic models. It supports 2PL, 3PL, and 4PL models via the model option.

result.IRT <- IRT(J15S500, model = 3)
result.IRT

The estimated ability parameters for each examinee are included in the returned object:

head(result.IRT$ability)

Plot Types

IRT provides several plot types:

• IRF: Item Response Function (Item Characteristic Curves)
• IIC: Item Information Curves
• TRF: Test Response Function
• TIC: Test Information Curve

Items can be specified using the items argument. The layout is controlled by nr (rows) and nc (columns).

plot(result.IRT, type = "IRF", items = 1:6, nc = 2, nr = 3)

plot(result.IRT, type = "IRF", overlay = TRUE)

plot(result.IRT, type = "IIC", items = 1:6, nc = 2, nr = 3)

plot(result.IRT, type = "TRF")

plot(result.IRT, type = "TIC")

GRM: Graded Response Model

The Graded Response Model (Samejima, 1969) extends IRT to polytomous response data. It can be applied using the GRM() function.

result.GRM <- GRM(J5S1000)
result.GRM

GRM supports similar plot types as IRT:

plot(result.GRM, type = "IRF", nc = 2)

plot(result.GRM, type = "IIF", nc = 2)

plot(result.GRM, type = "TIF")

References

• Shojima, K. (2022). Test Data Engineering. Springer.
• Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika, 34(S1), 1--97.

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