mycaas (version 0.0.1)

half_split: Questioning rule (half split)

Description

Rule to select the most informative item at each step of the assessment.

Usage

half_split(likelihood, states, beta, eta, Q_pool = NA)

Value

The item that maximizes the information (for details see, Doignon and Falmagne, 2012).

Arguments

likelihood

A vector of the likelihood distribution on the states in the structure.

states

A state-by-problem matrix representing the structure, where an element is one if the item is included in the state, and zero otherwise.

beta

Vector of careless error probabilities.

eta

Vector of lucky guess error probabilities.

Q_pool

A vector contains the pool of items for the assessment in this moment of the procedure.

References

Doignon, J.-P., & Falmagne, J.-C. (1999). Knowledge spaces. Berlin: Springer.

Examples

# Consider the knowledge space and the parameters used in Brancaccio,
# de Chiusole, Stefanutti (2023) in Example 1

states<-matrix(c( 0,0,0,0,0,
                   0,0,0,0,1,
                   0,0,1,0,1,
                   0,0,0,1,1,
                   0,0,1,1,1,
                   1,0,1,0,1,
                   0,1,0,1,1,
                   1,0,1,1,1,
                   0,1,1,1,1,
                   1,1,0,1,1,
                   1,1,1,1,1), byrow=TRUE, ncol=5)
beta  <-c(.004,.03,.02,.01,.007)
eta   <-c(5e-06, 5e-05, 4e-05,.007,.08)
likelihood <-c(0,0,0,0,0,1/3,0,1/3,0,0,1/3)
Q_pool <- c(2,4,5)
half_split(likelihood,states,beta,eta,Q_pool)