Caculate true-positive rate (TPR)

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.

Value

A numeric (TPR index).

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.

Examples

library(Qval)

set.seed(123)

example.Q1 <- sim.Q(5, 30)
example.Q2 <- sim.MQ(example.Q1, 0.1)
#> rate of mis-specifications =  0.1 
#>  rate of  over-specifications =  0.07 
#>  rate of under-specifications =  0.03 
example.Q3 <- sim.MQ(example.Q1, 0.05)
#> rate of mis-specifications =  0.05 
#>  rate of  over-specifications =  0.03 
#>  rate of under-specifications =  0.01 
TPR <- zTPR(example.Q1, example.Q2, example.Q3)

print(TPR)
#> [1] 0.9481481