mycaas (version 0.0.1)

updating: Updating rules

Description

Multiplicative rule as in Falmagne and Doignon 2010 (Chapter 13, Section 10)

Usage

updating(likelihood, states, q, r_q, beta, eta)

Value

The updated likelihood distribution on the knowledge states

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.

q

Last administered item

r_q

Observed response to item q

beta

Vector of careless error probabilities

eta

Vector of lucky guess error probabilities

Examples

# Let 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_0 <-rep(1,nrow(states))/nrow(states)
# Item asked
q = 3
# response observed
r_q = 1
likelihood_1 <- updating(likelihood_0,states,q,r_q,beta,eta)