ItemThreshold: Item Threshold

In exametrika: Test Theory Analysis and Biclustering

Item Threshold

Description

Item threshold is a measure of difficulty based on a standard normal distribution. This function is applicable only to binary response data.

The threshold is calculated as:

\tau_j = \Phi^{-1}(1-p_j)

where \Phi^{-1} is the inverse standard normal distribution function and p_j is the correct response rate for item j.

Higher threshold values indicate more difficult items, as they represent the point on the standard normal scale above which examinees tend to answer incorrectly.

Usage

ItemThreshold(U, na = NULL, Z = NULL, w = NULL)

## S3 method for class 'binary'
ItemThreshold(U, na = NULL, Z = NULL, w = NULL)

## S3 method for class 'ordinal'
ItemThreshold(U, na = NULL, Z = NULL, w = NULL)

Arguments

U	Either an object of class "exametrika" or raw data. When raw data is given, it is converted to the exametrika class with the dataFormat function.
na	Values to be treated as missing values.
Z	Missing indicator matrix of type matrix or data.frame. Values of 1 indicate observed responses, while 0 indicates missing data.
w	Item weight vector specifying the relative importance of each item.

Value

A numeric vector of threshold values for each item on the standard normal scale. Typical values range from about -3 to 3, where:

• Positive values indicate difficult items

• Zero indicates items of medium difficulty (50% correct)

• Negative values indicate easy items

Note

This function is implemented using a binary data compatibility wrapper and will raise an error if used with polytomous data.

Examples

# using sample dataset
ItemThreshold(J5S10)

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