gdd: Generalized Distance Discriminating Method

In CDM: Cognitive Diagnosis Modeling

Generalized Distance Discriminating Method

Description

Performs the generalized distance discriminating method (GDD; Sun, Xin, Zhang, & de la Torre, 2013) for dichotomous data which is a method for classifying students into skill profiles based on a preliminary unidimensional calibration.

Usage

gdd(data, q.matrix, theta, b, a, skillclasses=NULL)

Arguments

data	Data frame with N \times J item responses
q.matrix	The Q-matrix
theta	Estimated person ability
b	Estimated item intercept from a 2PL model (see Details)
a	Estimated item slope from a 2PL model (see Details)
skillclasses	Optional matrix of skill classes used for estimation

Details

Note that the parameters in the arguments follow the item response model

logit P( X_{nj}=1 | θ_n )=b_j + a_j θ_n

which is employed in the gdm function.

Value

A list with following entries

skillclass.est	Estimated skill class
distmatrix	Distances for every person and every skill class
skillspace	Used skill space for estimation
theta	Used person parameter estimate

References

Sun, J., Xin, T., Zhang, S., & de la Torre, J. (2013). A polytomous extension of the generalized distance discriminating method. Applied Psychological Measurement, 37, 503-521.

Examples

#############################################################################
# EXAMPLE 1: GDD for sim.dina
#############################################################################

data(sim.dina, package="CDM")
data(sim.qmatrix, package="CDM")

data <- sim.dina
q.matrix <- sim.qmatrix

# estimate 1PL (use irtmodel="2PL" for 2PL estimation)
mod <- CDM::gdm( data, irtmodel="1PL", theta.k=seq(-6,6,len=21),
                    decrease.increments=TRUE, conv=.001, globconv=.001)
# extract item parameters in parametrization b + a*theta
b <- mod$b[,1]
a <- mod$a[,,1]
# extract person parameter estimate
theta <- mod$person$EAP.F1

# generalized distance discriminating method
res <- CDM::gdd( data, q.matrix, theta=theta, b=b, a=a )

CDM documentation built on Aug. 25, 2022, 5:08 p.m.