CDM: din.equivalent.class – R documentation

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din.equivalent.class

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

Cognitive Diagnosis Modeling

v7.5-15

GPL (>= 2)

Authors

Alexander Robitzsch [aut, cre], Thomas Kiefer [aut], Ann Cathrice George [aut], Ali Uenlue [aut]

Initial release

2020-03-10 14:19:21