IRT: Estimating Item parameters using EM algorithm

In exametrika: Test Theory Analysis and Biclustering

Estimating Item parameters using EM algorithm

Description

A function for estimating item parameters using the EM algorithm.

Usage

IRT(U, model = 2, na = NULL, Z = NULL, w = NULL, verbose = TRUE)

Arguments

U	U is either a data class of exametrika, or raw data. When raw data is given, it is converted to the exametrika class with the dataFormat function.
model	This argument takes the number of item parameters to be estimated in the logistic model. It is limited to values 2, 3, or 4.
na	na argument specifies the numbers or characters to be treated as missing values.
Z	Z is a missing indicator matrix of the type matrix or data.frame
w	w is item weight vector
verbose	logical; if TRUE, shows progress of iterations (default: TRUE)

Details

Apply the 2, 3, and 4 parameter logistic models to estimate the item and subject populations. The 4PL model can be described as follows.

P(\theta,a_j,b_j,c_j,d_j)= c_j + \frac{d_j -c_j}{1+exp\{-a_j(\theta - b_j)\}}

a_j, b_j, c_j, and d_j are parameters related to item j, and are parameters that adjust the logistic curve. a_j is called the slope parameter, b_j is the location, c_j is the lower asymptote, and d_j is the upper asymptote parameter. The model includes lower models, and among the 4PL models, the case where d=1 is the 3PL model, and among the 3PL models, the case where c=0 is the 2PL model.

Value

model

number of item parameters you set.

testlength

Length of the test. The number of items included in the test.

nobs

Sample size. The number of rows in the dataset.

params

Matrix containing the estimated item parameters

Q3mat

Q3-matrix developed by Yen(1984)

itemPSD

Posterior standard deviation of the item parameters

ability

Estimated parameters of students ability

ItemFitIndices

Fit index for each item.See also ItemFit

TestFitIndices

Overall fit index for the test.See also TestFit

References

Yen, W. M. (1984) Applied Psychological Measurement, 8, 125-145.

Examples

# Fit a 3-parameter IRT model to the sample dataset
result.IRT <- IRT(J15S500, model = 3)

# Display the first few rows of estimated student abilities
head(result.IRT$ability)

# Plot Item Response Function (IRF) for items 1-6 in a 2x3 grid
plot(result.IRT, type = "IRF", items = 1:6, nc = 2, nr = 3)

# Plot Item Information Function (IIF) for items 1-6 in a 2x3 grid
plot(result.IRT, type = "IIF", items = 1:6, nc = 2, nr = 3)

# Plot the Test Information Function (TIF) for all items
plot(result.IRT, type = "TIF")

exametrika documentation built on Aug. 21, 2025, 5:27 p.m.