Caculate under-specifcation rate (USR)

Caculate under-specifcation rate (USR)

zUSR(Q.true, Q.sug)

Arguments

Q.true

The true Q-matrix.

Q.sug

A The Q-matrix that has being validated.

Value

A numeric (USR index).

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.

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 
USR <- zUSR(example.Q1, example.Q2)
print(USR)
#> [1] 0.02666667