<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: Calculation of Equivalent Skill Classes in the DINA/DINO...</title>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<link rel="stylesheet" type="text/css" href="R.css" />
</head><body>

<table width="100%" summary="page for din.equivalent.class"><tr><td>din.equivalent.class</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>
Calculation of Equivalent Skill Classes in the DINA/DINO Model
</h2>

<h3>Description</h3>

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


<h3>Usage</h3>

<pre>
din.equivalent.class(q.matrix, rule="DINA")
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>q.matrix</code></td>
<td>
<p>The Q-matrix (see <code>din</code>).</p>
</td></tr>
<tr valign="top"><td><code>rule</code></td>
<td>

<p>The condensation rule. If it is a string, then the rule applies
to all items. If it is a vector, then for each item <code>DINA</code>
or <code>DINO</code> rule can be chosen.
</p>
</td></tr>
</table>


<h3>Value</h3>

<p>A list with following entries:
</p>
<table summary="R valueblock">
<tr valign="top"><td><code>latent.responseM</code></td>
<td>
<p>Matrix of latent responses</p>
</td></tr>
<tr valign="top"><td><code>latent.response</code></td>
<td>
<p>Latent responses represented as a string</p>
</td></tr>
<tr valign="top"><td><code>S</code></td>
<td>
<p>Matrix containing all skill classes</p>
</td></tr>
<tr valign="top"><td><code>gini</code></td>
<td>
<p>Gini coefficient of the frequency distribution of
identifiable skill classes which result in the same latent response
</p>
</td></tr>
<tr valign="top"><td><code>skillclasses</code></td>
<td>
<p>Data frame with skill class (<code>skillclass</code>),
latent responses (<code>latent.response</code>) and an identifier for
distinguishable skill classes (<code>distinguish.class</code>).
</p>
</td></tr>
</table>


<h3>References</h3>

<p>Gross, J. &amp; George, A. C. (2014). On prerequisite relations between
attributes in noncompensatory diagnostic classification.
<em>Methodology, 10</em>(3), 100-107.
</p>
<p>Zhang, S. S., DeCarlo, L. T., &amp; Ying, Z. (2013).
Non-identifiability, equivalence classes, and attribute-specific classification
in Q-matrix based cognitive diagnosis models.
<em>arXiv preprint</em>, <em>arXiv:1303.0426</em>.
</p>


<h3>Examples</h3>

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

#-- DINA models

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

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

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

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

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


</body></html>
