gdd function

Generalized Distance Discriminating Method

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.

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

which is employed in the gdm function.

Returns

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 )