mycaas (version 0.0.1)

stopping_criterion: Stopping rule

Description

Rule to decide when terminate the assessment

Usage

stopping_criterion(
  likelihood,
  states,
  termination = "likelihood_maximization",
  SC = c(0.8)
)

Value

Return TRUE if the assessment should terminates under the criteria, otherwise FALSE

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.

termination

Define and select one of the termination criteria: "likelihood_maximization" the assessment terminates when the likelihood of a knowledge state in a knowledge structure became higher of the termination criteria (Heller, and Repitsch, 2012). "items_discrimination" the assessment terminates if the marginal likelihood of all the items is outside the interval of the stopping criteria (Donadello, Spoto, Sambo, Badaloni, Granziol, Vidotto, 2017).

SC

The Stopping criterion for the assessment is a numeric vector of values between 0 and 1. When the "termination" parameter is "likelihood_maximization" this is a single scalar that corresponds to the likelihood that a knowledge state needed to terminates the assessment. When the "termination" parameter is "items_discrimination" this is a numeric vector of length two, the assessment terminate if the the marginal likelihood of each item is outside of the interval between the two elements.

References

Donadello, I., Spoto, A., Sambo, F., Badaloni, S., Granziol, U., & Vidotto, G. (2017). ATS-PD: An adaptive testing system for psychological disorders. Educational and psychological measurement, 77(5), 792-815.

Heller, J., & Repitsch, C. (2012). Exploiting prior information in stochastic knowledge assessment. Methodology.

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(0,0,0,0,0,0,0,.49,0,0,.51)
#stopping criterion based on the likelihood mode
stopping_criterion(likelihood,states, termination="likelihood_maximization" ,SC=c(0.5))
#stopping criterion based on the items marginal probabilities
stopping_criterion(likelihood,states, termination="items_discrimination" ,SC=c(0.2,0.8))