zTPR: Calculate true-positive rate (TPR)

In Qval: The Q-Matrix Validation Methods Framework

Calculate true-positive rate (TPR)

Description

Calculate true-positive rate (TPR)

Usage

zTPR(Q.true, Q.orig, Q.sug)

Arguments

Q.true	The true Q-matrix.
Q.orig	The Q-matrix need to be validated.
Q.sug	The Q-matrix that has being validated.

Details

TPR is defned as the proportion of correct elements which are correctly retained:

TPR = \frac{\sum_{i=1}^{I}\sum_{k=1}^{K}I(q_{ik}^{t} = q_{ik}^{s} | q_{ik}^{t} = q_{ik}^{o})} {\sum_{i=1}^{I}\sum_{k=1}^{K}I(q_{ik}^{t} = q_{ik}^{o})}

where q_{ik}^{t} denotes the kth attribute of item i in the true Q-matrix (Q.true), q_{ik}^{o} denotes kth attribute of item i in the original Q-matrix(Q.orig), 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 (TPR index).

Examples

library(Qval)

set.seed(123)

example.Q1 <- sim.Q(5, 30)
example.Q2 <- sim.MQ(example.Q1, 0.1)
example.Q3 <- sim.MQ(example.Q1, 0.05)
TPR <- zTPR(example.Q1, example.Q2, example.Q3)

print(TPR)

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