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<p class="MsoNormal"><span style="color:#1F497D">I think it&#8217;s reasonable to assume the items are locally independent so I would go for scoring method #1.&nbsp; The other two methods loose information concerning e.g., item fit, person fit, etc.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"><o:p>&nbsp;</o:p></span></p>
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<p class="MsoNormal"><b><span style="font-size:10.0pt;font-family:&quot;Tahoma&quot;,&quot;sans-serif&quot;">From:</span></b><span style="font-size:10.0pt;font-family:&quot;Tahoma&quot;,&quot;sans-serif&quot;"> rasch-bounces@acer.edu.au [mailto:rasch-bounces@acer.edu.au]
<b>On Behalf Of </b>Fidelman, Carolyn<br>
<b>Sent:</b> Thursday, December 13, 2012 9:32 AM<br>
<b>To:</b> rasch@acer.edu.au<br>
<b>Subject:</b> [Rasch] Reverse Digit Span Item Scoring Question<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal">HI All,<o:p></o:p></p>
<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal">We are considering creating our own scale for a reverse digit span task that is to be administered to children ages 5-11 longitudinally and I am having trouble understanding which Rasch model to use or how to structure the data.&nbsp;
<o:p></o:p></p>
<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal">What is done in such a test is that a child is first asked to repeat back two numbers that they hear on an audio recording, but in reverse order. They get five such items and, if they get three of them right, they go on to the next level.
 Each level consists of an additional number of numbers to repeat back all the way up to 9. Most adults can do about 7. This is correlated to general intelligence and is predictive of a number of achievement related outcomes. This is modeled off of something
 from the Woodcock Johnson COG III called Numbers Reversed and is Test 7 in their battery of cognitive assessments.&nbsp;
<o:p></o:p></p>
<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal">My hope was that the WJ documentation would tell us which Rasch model was used with this &#8220;trials&#8221;-type data. But it doesn&#8217;t really go into it, perhaps for proprietary reasons? It says that the original calibration program was devised by
 Woodcock in approximately 1970. Much has been done to develop models that fit various data types since that time.&nbsp; It is not clear what the Woodcock procedure is exactly and how it differs from or is similar to standard Rasch 1 parameter, rating scale&nbsp; or
 partial credit model.&nbsp; I am concerned about this because we need to decide whether the structure of the data is to be discrete or clustered and determine whether it is also a problem that it is hierarchical where performances are nested within type.<o:p></o:p></p>
<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal">One question I have for this test is &#8220;What is an item?&#8221;&nbsp; Is an item a single trial or the &nbsp;5-trial (4-trial later on) cluster? How is that scored for the purposes of score calibration? Is it a 0,1 for each trial or is it a scale from 0-5
 (0-4 later on) for each cluster? Would we lose too much information going to a polytomous scoring? &nbsp;The administration protocol is that if the child gets three in a cluster such as the two-numbers type, they move on to the next greater number type. If they
 only get two in a cluster, they are considered to have achieved that span but not more and no further items are presented.<o:p></o:p></p>
<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal">Item type/names by number of digits to recall:<o:p></o:p></p>
<p class="MsoNoSpacing" style="margin-left:.25in"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:yellow;mso-highlight:yellow">22222</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:lime;mso-highlight:lime">33333</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:aqua;mso-highlight:aqua">4444</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:fuchsia;mso-highlight:fuchsia">5555</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:silver;mso-highlight:silver">6666</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:yellow;mso-highlight:yellow">7777</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:lime;mso-highlight:lime">8888</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:aqua;mso-highlight:aqua">9999</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;"><o:p></o:p></span></p>
<p class="MsoNoSpacing" style="margin-left:.25in"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal">Example item scorings:<o:p></o:p></p>
<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal">1. One record of a discrete, dichotomously scored raw score file:<o:p></o:p></p>
<p class="MsoNoSpacing" style="margin-left:.25in"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:yellow;mso-highlight:yellow">11111</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:lime;mso-highlight:lime">11110</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:aqua;mso-highlight:aqua">1110</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:fuchsia;mso-highlight:fuchsia">0008</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:silver;mso-highlight:silver">8888</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:yellow;mso-highlight:yellow">8888</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:lime;mso-highlight:lime">8888</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:aqua;mso-highlight:aqua">8888</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;">*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 &nbsp;&nbsp;&nbsp;*8=not presented<o:p></o:p></span></p>
<p class="MsoNoSpacing" style="margin-left:.25in"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal">2. One record of a clustered, dichotomously scored file:<o:p></o:p></p>
<p class="MsoNoSpacing" style="margin-left:.25in"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:yellow;mso-highlight:yellow">1</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:lime;mso-highlight:lime">1</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:aqua;mso-highlight:aqua">1</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:fuchsia;mso-highlight:fuchsia">0</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:silver;mso-highlight:silver">8</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:yellow;mso-highlight:yellow">8</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:lime;mso-highlight:lime">8</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:aqua;mso-highlight:aqua">8</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;"><o:p></o:p></span></p>
<p class="MsoNoSpacing" style="margin-left:.25in"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal">3. One record of a clustered, polytomously scored file:<o:p></o:p></p>
<p class="MsoNoSpacing" style="margin-left:.25in"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:yellow;mso-highlight:yellow">5</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:lime;mso-highlight:lime">4</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:aqua;mso-highlight:aqua">3</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:fuchsia;mso-highlight:fuchsia">0</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:silver;mso-highlight:silver">8</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:yellow;mso-highlight:yellow">8</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:lime;mso-highlight:lime">8</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;background:aqua;mso-highlight:aqua">8</span><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;"><o:p></o:p></span></p>
<p class="MsoNoSpacing" style="margin-left:.25in"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal">What we have seen in other ECLS tests is that when we violate the assumption of local item independence, through either a prompt or format effect, item parameters can be inflated and standard errors artificially low or unstable. A possible
 further violation in this case is that of not taking into account the extra variability between levels of data in a hierarchy, in addition to those within item sets.<o:p></o:p></p>
<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal">Does anyone here know informally or through some publication source(1), what exact Rasch model the WJ folks used for this test? Or, regardless of that, what do you think one would do here? I am not comfortable with just treating it as in
 example 1 above.&nbsp; Thanks for any help you can offer!<o:p></o:p></p>
<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal">Carolyn<o:p></o:p></p>
<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal"><span lang="EN" style="font-size:9.0pt;font-family:&quot;Courier New&quot;">Carolyn G. Fidelman, Ph.D.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:&quot;Courier New&quot;">Early Childhood, International &amp; Crosscutting Studies</span><span lang="EN" style="font-size:9.0pt;font-family:&quot;Courier New&quot;">, NCES<br>
Rm 9035, 1990 K St. NW | 202-502-7312 | </span><a href="mailto:carolyn.fidelman@ed.gov"><span lang="EN" style="font-size:9.0pt;font-family:&quot;Courier New&quot;;color:windowtext">carolyn.fidelman@ed.gov</span></a><span style="font-size:9.0pt;font-family:&quot;Courier New&quot;">
<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
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<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal">(1) I consulted the following: <o:p></o:p></p>
<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
<p class="MsoNormal"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;">Jaffe, L. E. (2009).<i> Development, interpretation, and application of the W score and the relative proficiency index</i> (Woodcock-Johnson III Assessment Service Bulletin No. 11). Rolling
 Meadows, IL: Riverside Publishing.<o:p></o:p></span></p>
<p class="MsoNoSpacing" style="margin-left:.25in"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNoSpacing" style="margin-left:.25in"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;">and
<o:p></o:p></span></p>
<p class="MsoNoSpacing" style="margin-left:.25in"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNoSpacing"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;">McGrew, K., Schrank, F., Woodcock, R. (2007). Woodcock-Johnson Normative Update: Technical Manual. Rolling Meadows, IL: Riverside Publishing.<o:p></o:p></span></p>
<p class="MsoNoSpacing" style="margin-left:.25in"><span style="font-family:&quot;Times New Roman&quot;,&quot;serif&quot;"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><o:p>&nbsp;</o:p></p>
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