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<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Tom, it depends on the reason you
constructed the items with the intention of producing 'consistent'
thresholds, by which I assume you mean that each threshold has the same
distance from the central (item) location for every item. Unless it is critical
to your research objectives that the thresholds are consistent, I would look at
the evidence to try to ascertain whether there is better fit to the model when
each item is allowed to have different (centralised) thresholds, given the
additional parameters. I would look at any evidence available about fit
including graphical information such as ICCs. Generally speaking, I would be
more concerned about which collection of items measure the latent trait(s) than
whether the thresholds are necessarily consistent, although it depends on your objectives.</span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>&nbsp;</span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Disordered thresholds indicate a problem with
the data elicited by the relevant items, because the formal structure of the
model entails a latent Guttman response subspace, which in turn entails ordered
thresholds (</span></font><font size=2 color=navy face=Arial><span
 style='font-size:10.0pt;font-family:Arial;color:navy'>Andrich</span></font><font
size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'>, 1978, 2005). Integer scoring is a classification process in which
a score of x implies that: (i) the x lowest thresholds are exceeded and,
simultaneously, that; (ii) the m - x highest thresholds are not exceeded
(where m is the maximum score for the item). It is always a hypothesis that the
thresholds are ordered given the nature of response categories comprising an
item, and it is empirically possible for the threshold estimates not to be in
their natural order; i.e. the hypothesis is refutable.</span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>&nbsp;</span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>&nbsp;</span></font></p>

<p class=MsoNormal style='background:#F8FCFF'><font size=3
 face="Times New Roman"><span lang=EN style='font-size:12.0pt'>Andrich</span></font><span
lang=EN>, D. (1978). A rating formulation for ordered response categories. <i><span
style='font-style:italic'>Psychometrika</span></i>, 43, 357-74.</span></p>

<p class=MsoNormal style='background:#F8FCFF'><font size=3
face="Times New Roman"><span lang=EN style='font-size:12.0pt'>&nbsp;</span></font></p>

<p class=MsoNormal style='background:#F8FCFF'><font size=3
 face="Times New Roman"><span lang=EN style='font-size:12.0pt'>Andrich</span></font><span
lang=EN>, D. (2005). The Rasch model explained. In Sivakumar Alagumalai, David
D Durtis, and Njora Hungi (Eds.) <i><span style='font-style:italic'>Applied
Rasch Measurement: A book of exemplars</span></i>. Springer-Kluwer. Chapter 3,
308-328. </span></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>&nbsp;</span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Steve</span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>&nbsp;</span></font></p>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>&nbsp;</span></font></p>

<div>

<p class=MsoNormal><font size=2 color="#333399" face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:#333399'>Stephen Humphry, PhD</span></font></p>

<p class=MsoNormal><font size=2 color="#333399" face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:#333399'>Senior Educational
Measurement Officer, Psychometrics</span></font></p>

<p class=MsoNormal><font size=2 color="#333399" face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:#333399'>Department of
Education &amp; Training</span></font></p>

<p class=MsoNormal><font
  size=2 color="#333399" face=Arial><span style='font-size:10.0pt;font-family:
  Arial;color:#333399'>151 Royal Street, East</span></font><font size=2
 color="#333399" face=Arial><span style='font-size:10.0pt;font-family:Arial;
 color:#333399'> </span></font><font size=2 color="#333399" face=Arial><span
  style='font-size:10.0pt;font-family:Arial;color:#333399'>Perth</span></font><font
size=2 color="#333399" face=Arial><span style='font-size:10.0pt;font-family:
Arial;color:#333399'>, 6004</span></font></p>

<p class=MsoNormal><font size=3 color="#333399" face="Times New Roman"><span
style='font-size:12.0pt;color:#333399'>&nbsp;</span></font></p>

<p class=MsoNormal><font size=2 color="#333399" face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:#333399'>Phone: +61 8 92644102</span></font></p>

</div>

<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>&nbsp;</span></font></p>

<p class=MsoNormal style='margin-left:36.0pt'><font size=2 face=Tahoma><span
lang=EN-US style='font-size:10.0pt;font-family:Tahoma'>-----Original
Message-----<br>
<b><span style='font-weight:bold'>From:</span></b> rasch-bounces@acer.edu.au
[mailto:rasch-bounces@acer.edu.au] <b><span style='font-weight:bold'>On Behalf
Of </span></b>Snider-Lotz, Tom<br>
<b><span style='font-weight:bold'>Sent:</span></b> </span></font><font size=2 face=Tahoma><span lang=EN-US style='font-size:10.0pt;font-family:Tahoma'>Wednesday,
 17 May 2006</span></font><font size=2 face=Tahoma><span lang=EN-US
style='font-size:10.0pt;font-family:Tahoma'> </span></font><font
 size=2 face=Tahoma><span lang=EN-US style='font-size:10.0pt;font-family:Tahoma'>8:59
 AM</span></font><font size=2 face=Tahoma><span lang=EN-US style='font-size:
10.0pt;font-family:Tahoma'><br>
<b><span style='font-weight:bold'>To:</span></b> rasch@acer.edu.au<br>
<b><span style='font-weight:bold'>Subject:</span></b> [Rasch] Rating Scale or
Partial Credit?</span></font></p>

<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>&nbsp;</span></font></p>

<div id=idOWAReplyText61575>

<div>

<div>

<p class=MsoNormal style='margin-left:36.0pt'><font size=2 color=navy
face=Verdana><span style='font-size:10.0pt;font-family:Verdana;color:navy'>Hello
everyone --</span></font></p>

</div>

<div>

<p class=MsoNormal style='margin-left:36.0pt'><font size=2 color=navy
face=Verdana><span style='font-size:10.0pt;font-family:Verdana;color:navy'>&nbsp;</span></font></p>

</div>

<div>

<p class=MsoNormal style='margin-left:36.0pt'><font size=2 color=navy
face=Verdana><span style='font-size:10.0pt;font-family:Verdana;color:navy'>I am
analyzing data from a personality instrument that employs 5-option Likert-style
items.&nbsp; Inspection of the results shows that the items vary greatly in terms
of how well-spaced and well-ordered their thresholds are.&nbsp; Should I be
using a partial credit model, because empirically I know the thresholds are
different for each item?&nbsp; Or should I use a rating scale model, because
the items were created with the intention of
producing&nbsp;consistent&nbsp;thresholds?</span></font></p>

</div>

<div>

<p class=MsoNormal style='margin-left:36.0pt'><font size=2 color=navy
face=Verdana><span style='font-size:10.0pt;font-family:Verdana;color:navy'>&nbsp;</span></font></p>

</div>

<div>

<p class=MsoNormal style='margin-left:36.0pt'><font size=2 color=navy
face=Verdana><span style='font-size:10.0pt;font-family:Verdana;color:navy'>Thanks.</span></font></p>

</div>

<div>

<p class=MsoNormal style='margin-left:36.0pt'><font size=2 color=navy
face=Verdana><span style='font-size:10.0pt;font-family:Verdana;color:navy'>&nbsp;</span></font></p>

</div>

<div>

<p class=MsoNormal style='margin-left:36.0pt'><font size=2 color=navy
face=Verdana><span style='font-size:10.0pt;font-family:Verdana;color:navy'>&nbsp;
-- Tom Snider-Lotz</span></font></p>

</div>

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face="Times New Roman"><span style='font-size:12.0pt'>&nbsp;</span></font></p>

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<p class=MsoNormal style='margin-left:36.0pt'><font size=2 color=black
face="Times New Roman"><span style='font-size:10.0pt;color:black'>___________________________________</span></font></p>

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<p class=MsoNormal style='margin-left:36.0pt'><font size=2 color=black
face="Times New Roman"><span style='font-size:10.0pt;color:black'>Thomas G.
Snider-Lotz, Ph.D.</span></font></p>

</div>

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