din.equivalent.class: Calculation of Equivalent Skill Classes in the DINA/DINO...

In CDM: Cognitive Diagnosis Modeling

Calculation of Equivalent Skill Classes in the DINA/DINO Model

Description

This function computes indistinguishable skill classes for the DINA and DINO model (Gross & George, 2014; Zhang, DeCarlo & Ying, 2013).

Usage

din.equivalent.class(q.matrix, rule="DINA")

Arguments

q.matrix	The Q-matrix (see din).
rule	The condensation rule. If it is a string, then the rule applies to all items. If it is a vector, then for each item DINA or DINO rule can be chosen.

Value

A list with following entries:

latent.responseM	Matrix of latent responses
latent.response	Latent responses represented as a string
S	Matrix containing all skill classes
gini	Gini coefficient of the frequency distribution of identifiable skill classes which result in the same latent response
skillclasses	Data frame with skill class (skillclass), latent responses (latent.response) and an identifier for distinguishable skill classes (distinguish.class).

References

Gross, J. & George, A. C. (2014). On prerequisite relations between attributes in noncompensatory diagnostic classification. Methodology, 10(3), 100-107.

Zhang, S. S., DeCarlo, L. T., & Ying, Z. (2013). Non-identifiability, equivalence classes, and attribute-specific classification in Q-matrix based cognitive diagnosis models. arXiv preprint, arXiv:1303.0426.

Examples

#############################################################################
# EXAMPLE 1: Equivalency classes for DINA model for fraction subtraction data
#############################################################################

#-- DINA models

data(data.fraction2, package="CDM")

# first Q-matrix
Q1 <- data.fraction2$q.matrix1
m1 <- CDM::din.equivalent.class( q.matrix=Q1, rule="DINA" )
  ## 8 Skill classes | 5  distinguishable skill classes | Gini coefficient=0.3

# second Q-matrix
Q1 <- data.fraction2$q.matrix2
m1 <- CDM::din.equivalent.class( q.matrix=Q1, rule="DINA" )
  ## 32 Skill classes | 9  distinguishable skill classes | Gini coefficient=0.5

# third Q-matrix
Q1 <- data.fraction2$q.matrix3
m1 <- CDM::din.equivalent.class( q.matrix=Q1, rule="DINA" )
  ## 8 Skill classes | 8  distinguishable skill classes | Gini coefficient=0

# original fraction subtraction data
m1 <- CDM::din.equivalent.class( q.matrix=CDM::fraction.subtraction.qmatrix, rule="DINA")
  ## 256 Skill classes | 58  distinguishable skill classes | Gini coefficient=0.659

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