zUSR: Calculate under-specifcation rate (USR)

In Qval: The Q-Matrix Validation Methods Framework

Calculate under-specifcation rate (USR)

Description

Calculate under-specifcation rate (USR)

Usage

zUSR(Q.true, Q.sug)

Arguments

Q.true	The true Q-matrix.
Q.sug	The Q-matrix that has being validated.

Details

The USR is defned as:

USR = \frac{\sum_{i=1}^{I}\sum_{k=1}^{K}I(q_{ik}^{t} > q_{ik}^{s})}{I × K}

where q_{ik}^{t} denotes the kth attribute of item i in the true Q-matrix (Q.true), q_{ik}^{s} denotes kth attribute of item i in the suggested Q-matrix(Q.sug), and I(\cdot) is the indicator function.

Value

A numeric (USR index).

Examples

library(Qval)

set.seed(123)

example.Q1 <- sim.Q(5, 30)
example.Q2 <- sim.MQ(example.Q1, 0.1)
USR <- zUSR(example.Q1, example.Q2)
print(USR)

Qval documentation built on April 3, 2025, 6:20 p.m.