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    <div class="moz-cite-prefix">Thomas,<br>
      very good comments.<br>
      Luigi Tesio<br>
      <br>
      Il 26/10/13 18:34, Thomas Salzberger ha scritto:<br>
    </div>
    <blockquote
cite="mid:CAK5c+O8UtBmCdxL6WE3XpAmLd53UacrwVVLatb==F+JqUS7Adw@mail.gmail.com"
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                                  <div>Don &amp; Luis,<br>
                                    <br>
                                  </div>
                                  I fear Jack et al.'s paper on causal
                                  Rasch models is not exactly what Don
                                  looks for. The idea of a Causal RM is
                                  that one should identify the mechanism
                                  that drives measurement and
                                  experimentally manipulate item
                                  difficulty and person ability.<br>
                                  <br>
                                </div>
                                Formative "measurement", or "formative
                                indicators",  is something else. But
                                Jack has also commented on this (<a
                                  moz-do-not-send="true"
                                  href="http://www.rasch.org/rmt/rmt221d.htm">http://www.rasch.org/rmt/rmt221d.htm</a>).<br>
                                <br>
                              </div>
                              It does not surprise me that many Rasch
                              advocates know very little or nothing
                              about "formative measurement". And for a
                              good reason. <br>
                              In my mind, formative measurement is a
                              misconception, a fallacy (see Edwards: The
                              fallacy of formative measurement,
                              Organizational Research Methods <span
                                class="">2011 </span><span class="">
                                vol. 14 </span><span class=""> no. 2 </span><span
                                class=""> 370-38), and seriously
                                misleading.<br>
                                <br>
                              </span></div>
                            <span class="">Borsboom </span>(2003 <span
                              class="">The <em>Theoretical Status of
                                Latent Variables</em>. Denny Borsboom,
                              Gideon J. Mellenbergh, and Jaap van
                              Heerden in Psychological Review; 2005 book
                              Measuring the mind) has convincingly
                              demonstrated that the idea of a latent
                              variable (and thus, a unidimensional
                              construct) and formative "measurement" are
                              incompatible provided you are in the
                              realist camp. <br>
                              <br>
                            </span></div>
                          <span class="">If you critically question
                            Jarvis et al's rules for deciding whether
                            something has to be measured with reflective
                            indicators (-&gt; factor analysis in CTT,
                            IRT, Rasch) or formative indicators (-&gt; ?
                            what "model" would you actually use?), then
                            you notice that the criteria follow from
                            what you assume (reflective or formative) in
                            the first place. Yes, there sometimes is
                            indeed a misspecification, but it is not a
                            misspecification in terms of reflective
                            measurement vs formative measurement.
                            Rather, it is a misspecification with
                            respect to measurement vs the summary of
                            measurements. The latter essentially is a
                            structural model. <br>
                          </span></div>
                        <div><span class="">The reason why many people
                            have no problems accepting formative
                            measurement as measurement is probably due
                            to Stevens' definition of measurement. If
                            assigning numerals and interpreting them as
                            numbers is measurement, then of course
                            formative indicators also give you
                            measurement. But then anything goes.<br>
                          </span></div>
                        <div><span class=""><br>
                            <br>
                          </span><br>
                          <p class="MsoNormal">I was contacted by my
                            agent to make changes in my policy</p>
                          <p class="MsoNormal">I was contacted by my
                            agent to sell me more life insurance</p>
                          <p class="MsoNormal">I was contacted by my
                            agent to describe new insurance offerings</p>
                          I was contacted by my agent to keep my policy
                          in place<br>
                          <br>
                          <br>
                        </div>
                        This does not make any sense to me. If you are
                        interested in the intensity of contact, why not
                        just ask whether one was contacted?<br>
                      </div>
                      You may add reasons and that gives you additional
                      information. But these items do not form a scale,
                      and the sum score cannot lead to measurement.<br>
                      <br>
                    </div>
                    If I wanted to measure "subjective warmth", I would
                    not use the following items, would I:<br>
                    <br>
                  </div>
                  I feel warm because it is hot outside.<br>
                </div>
                I feel warm because the heating is on.<br>
              </div>
              I feel warm because I have a fever.<br>
              <br>
            </div>
            <br>
          </div>
          Best<br>
        </div>
        Thomas<br>
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                                      <br>
                                      <div class="gmail_quote">
                                        2013/10/26 Luis Carlos Orozco <span
                                          dir="ltr">&lt;<a
                                            moz-do-not-send="true"
                                            href="mailto:lcorovar@gmail.com"
                                            target="_blank">lcorovar@gmail.com</a>&gt;</span><br>
                                        <blockquote class="gmail_quote"
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                                          <div dir="ltr">There is a
                                            recent article in Frontiers
                                            in Psychology august 2013
                                            volume 4 by Stenner, Fisher,
                                            Stone , Burdick  "Causal
                                            Rasch models". That could
                                            help you.
                                            <div><br>
                                            </div>
                                            <div>Luis C. Orozco V. MD
                                              MSc</div>
                                            <div>Profesor Asociado</div>
                                            <div>Escuela de Enfermería</div>
                                            <div>Universidad Industrial
                                              de Santander</div>
                                            <div>Colombia</div>
                                            <div><br>
                                            </div>
                                          </div>
                                          <div class="gmail_extra"><br>
                                            <br>
                                            <div class="gmail_quote">2013/10/26
                                              Donald Bacon <span
                                                dir="ltr">&lt;<a
                                                  moz-do-not-send="true"
href="mailto:dbacon@du.edu" target="_blank">dbacon@du.edu</a>&gt;</span><br>
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                                                    <p class="MsoNormal">Hi
                                                      all --</p>
                                                    <p class="MsoNormal"> </p>
                                                    <p class="MsoNormal">To
                                                      offer more
                                                      explanation on my
                                                      reflective v.
                                                      formative
                                                      question, in
                                                      reflective
                                                      measurement
                                                      models, the
                                                      construct/latent
                                                      trait causes the
                                                      measures/indicators/items,
                                                      whereas in
                                                      formative models,
                                                      the measures cause
                                                      the latent trait. 
                                                      Jarvis, MacKenzie
                                                      and Podsakoff (J
                                                      Consumer Research,
                                                      2003) offer a
                                                      thorough
                                                      description of
                                                      this difference. 
                                                      They cite Bollen
                                                      and Lennox (Psych
                                                      Bull, 1991) as
                                                      identifying the
                                                      same distinction,
                                                      except that Bollen
                                                      and Lennox call
                                                      reflective
                                                      indicators
                                                      &#8216;effects
                                                      indicators&#8217; in a
                                                      principal
                                                      component model,
                                                      and formative
                                                      indicators &#8216;causal
                                                      indicators&#8217; in a
                                                      composite latent
                                                      construct model.</p>
                                                    <p class="MsoNormal"> </p>
                                                    <p class="MsoNormal">Jarvis
                                                      et al. cite a
                                                      formative example
                                                      from Crosby and
                                                      Stephens (1987)
                                                      that I will
                                                      paraphrase here. 
                                                      In measuring the
                                                      construct
                                                      &#8220;personal contact
                                                      with life
                                                      insurance agents&#8221;,
                                                      suppose the
                                                      following measures
                                                      are used:</p>
                                                    <p class="MsoNormal">I
                                                      was contacted by
                                                      my agent to make
                                                      changes in my
                                                      policy</p>
                                                    <p class="MsoNormal">I
                                                      was contacted by
                                                      my agent to sell
                                                      me more life
                                                      insurance</p>
                                                    <p class="MsoNormal">I
                                                      was contacted by
                                                      my agent to
                                                      describe new
                                                      insurance
                                                      offerings</p>
                                                    <p class="MsoNormal">I
                                                      was contacted by
                                                      my agent to keep
                                                      my policy in place</p>
                                                    <p class="MsoNormal"> </p>
                                                    <p class="MsoNormal">In
                                                      these items, the
                                                      agent would not
                                                      suggest keeping
                                                      the policy and
                                                      changing the
                                                      policy, so the
                                                      inter-item
                                                      correlations here
                                                      should be low or
                                                      perhaps even
                                                      negative, yet all
                                                      of these
                                                      statements
                                                      indicate personal
                                                      contact.  Internal
                                                      consistency is not
                                                      necessary for
                                                      formative
                                                      measures; to
                                                      assess the quality
                                                      of formative
                                                      measures we need
                                                      to look at
                                                      criterion-related
                                                      validity.  Thus,
                                                      formative models
                                                      are a bit more
                                                      like regression
                                                      models, where the
                                                      many independent
                                                      variables are
                                                      assumed to have no
                                                      error and may have
                                                      low
                                                      intercorrrelations
                                                      but the one
                                                      dependent variable
                                                      does have error.</p>
                                                    <p class="MsoNormal"> </p>
                                                    <p class="MsoNormal">Jarvis
                                                      et al. go on to
                                                      report how
                                                      measurement models
                                                      have often been
                                                      misspecified, even
                                                      in top marketing
                                                      journals, as
                                                      formative measures
                                                      have been treated
                                                      as reflective and
                                                      vice versa.  They
                                                      show how such
                                                      misspecification
                                                      can bias
                                                      structural path
                                                      estimates.  </p>
                                                    <p class="MsoNormal"> </p>
                                                    <p class="MsoNormal">Getting
                                                      back to Rasch
                                                      measurement, it
                                                      seems to me that
                                                      Rasch assumes a
                                                      reflective/effects/principal
                                                      components model. 
                                                      However, Rasch may
                                                      occasionally be
                                                      misapplied to
                                                      formative
                                                      indicators.  In
                                                      the latter case,
                                                      model fit and
                                                      internal
                                                      consistency would
                                                      probably be low,
                                                      but this is due
                                                      mainly to
                                                      fundamental model
                                                      misspecification. 
                                                      Or can Rasch be
                                                      used with
                                                      formative
                                                      indicators?</p>
                                                    <p class="MsoNormal"> </p>
                                                    <p class="MsoNormal">Has
                                                      this type of model
                                                      misspecification
                                                      been discussed in
                                                      the Rasch
                                                      literature?  More
                                                      specifically, are
                                                      all tests of
                                                      ability or
                                                      knowledge
                                                      generally
                                                      reflective
                                                      models?  Is there
                                                      a good cite that
                                                      someone can point
                                                      me too?
                                                    </p>
                                                    <p class="MsoNormal"> </p>
                                                    <p class="MsoNormal">Thanks
                                                      for any insights
                                                      you may be able to
                                                      provide.</p>
                                                    <p class="MsoNormal"><span
style="color:rgb(31,73,125)"> </span></p>
                                                    <p class="MsoNormal">Don</p>
                                                    <p class="MsoNormal"><span
style="color:rgb(31,73,125)"> </span></p>
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                                                        <p
                                                          class="MsoNormal"><b><span
style="font-size:10pt;font-family:&quot;Tahoma&quot;,&quot;sans-serif&quot;">From:</span></b><span
style="font-size:10pt;font-family:&quot;Tahoma&quot;,&quot;sans-serif&quot;">
                                                          <a
                                                          moz-do-not-send="true"
href="mailto:rasch-bounces@acer.edu.au" target="_blank">rasch-bounces@acer.edu.au</a>
                                                          [mailto:<a
                                                          moz-do-not-send="true"
href="mailto:rasch-bounces@acer.edu.au" target="_blank">rasch-bounces@acer.edu.au</a>]
                                                          <b>On Behalf
                                                          Of </b>Bond,
                                                          Trevor<br>
                                                          <b>Sent:</b>
                                                          Saturday,
                                                          October 26,
                                                          2013 1:17 AM<br>
                                                          <b>To:</b> <a
moz-do-not-send="true" href="mailto:rasch@acer.edu.au" target="_blank">rasch@acer.edu.au</a><br>
                                                          <b>Subject:</b>
                                                          Re: [Rasch]
                                                          formative v.
                                                          reflective
                                                          measures in
                                                          assessment
                                                          research</span></p>
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                                                        <p
                                                          class="MsoNormal"> </p>
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                                                          <p
                                                          class="MsoNormal"><span
style="font-size:10.5pt">Dear Donald,</span></p>
                                                        </div>
                                                        <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size:10.5pt">Perhaps you could share what you mean by
                                                          formative and
                                                          reflective, so
                                                          we might be
                                                          able better to
                                                          answer your
                                                          question.</span></p>
                                                        </div>
                                                        <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size:10.5pt">Collegially</span></p>
                                                        </div>
                                                        <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size:10.5pt">TGB</span></p>
                                                        </div>
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                                                          <p
                                                          class="MsoNormal"><span
style="font-size:10.5pt"> </span></p>
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                                                          <p
                                                          class="MsoNormal"><b><span>From:
                                                          </span></b><span>Donald
                                                          Bacon &lt;<a
                                                          moz-do-not-send="true"
href="mailto:dbacon@du.edu" target="_blank">dbacon@du.edu</a>&gt;<br>
                                                          <b>Reply-To: </b>"<a
moz-do-not-send="true" href="mailto:rasch@acer.edu.au" target="_blank">rasch@acer.edu.au</a>"
                                                          &lt;<a
                                                          moz-do-not-send="true"
href="mailto:rasch@acer.edu.au" target="_blank">rasch@acer.edu.au</a>&gt;<br>
                                                          <b>Date: </b>Saturday,
                                                          26 October
                                                          2013 3:57 AM<br>
                                                          <b>To: </b>"<a
moz-do-not-send="true" href="mailto:rasch@acer.edu.au" target="_blank">rasch@acer.edu.au</a>"
                                                          &lt;<a
                                                          moz-do-not-send="true"
href="mailto:rasch@acer.edu.au" target="_blank">rasch@acer.edu.au</a>&gt;<br>
                                                          <b>Subject: </b>[Rasch]
                                                          formative v.
                                                          reflective
                                                          measures in
                                                          assessment
                                                          research</span></p>
                                                        </div>
                                                        <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size:10.5pt"> </span></p>
                                                        </div>
                                                        <div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span>Hi
                                                          all &#8211;</span></p>
                                                          <p
                                                          class="MsoNormal"><span>  
                                                          The Rasch
                                                          model assumes
                                                          that each
                                                          measure in a
                                                          scale reflects
                                                          the same
                                                          underlying
                                                          trait, and so
                                                          it seems that
                                                          a reflective
                                                          measurement
                                                          model is
                                                          appropriate,
                                                          and internal
                                                          consistency is
                                                          a desirable
                                                          quality.  But
                                                          what about the
                                                          case of a long
                                                          comprehensive
                                                          exam, such as
                                                          one we might
                                                          use for
                                                          assessment. 
                                                          In my
                                                          experience,
                                                          these exams
                                                          often behave
                                                          as if they
                                                          were close to
                                                          unidimensional,
                                                          even though
                                                          many different
                                                          learning
                                                          outcomes are
                                                          captured.  If
                                                          well designed,
                                                          these tests
                                                          often exhibit
                                                          high internal
                                                          consistency.
                                                           Because the
                                                          models fit
                                                          well, I&#8217;ve
                                                          always thought
                                                          of the
                                                          measures as
                                                          reflective,
                                                          but perhaps my
                                                          theory is
                                                          wrong even
                                                          though the fit
                                                          is good; maybe
                                                          the measures
                                                          are
                                                          formative.  Is
                                                          there any way
                                                          to use the
                                                          Rasch model
                                                          with formative
                                                          indicators?</span></p>
                                                          <p
                                                          class="MsoNormal"><span> </span></p>
                                                          <p
                                                          class="MsoNormal"><span>Thanks
                                                          for any
                                                          insights you
                                                          might have &#8211;</span></p>
                                                          <p
                                                          class="MsoNormal"><span> </span></p>
                                                          <p
                                                          class="MsoNormal"><span>Don
                                                          </span></p>
                                                          <p
                                                          class="MsoNormal"><span> </span></p>
                                                          <p
                                                          class="MsoNormal"><span>Donald
                                                          R. Bacon,
                                                          Ph.D.</span></p>
                                                          <p
                                                          class="MsoNormal"><span>Professor
                                                          of Marketing</span></p>
                                                          <p
                                                          class="MsoNormal"><span>Editor,
                                                          Journal of
                                                          Marketing
                                                          Education</span></p>
                                                          <p
                                                          class="MsoNormal"><span>Daniels
                                                          College of
                                                          Business</span></p>
                                                          <p
                                                          class="MsoNormal"><span>University
                                                          of Denver</span></p>
                                                          <p
                                                          class="MsoNormal"><span> </span></p>
                                                          </div>
                                                        </div>
                                                      </div>
                                                    </div>
                                                  </div>
                                                </div>
                                                <br>
_______________________________________________<br>
                                                Rasch mailing list<br>
                                                <a
                                                  moz-do-not-send="true"
href="mailto:Rasch@acer.edu.au" target="_blank">Rasch@acer.edu.au</a><br>
                                                Unsubscribe: <a
                                                  moz-do-not-send="true"
href="https://mailinglist.acer.edu.au/mailman/options/rasch/lcorovar%40gmail.com"
                                                  target="_blank">https://mailinglist.acer.edu.au/mailman/options/rasch/lcorovar%40gmail.com</a><br>
                                              </blockquote>
                                            </div>
                                            <br>
                                          </div>
                                          <br>
_______________________________________________<br>
                                          Rasch mailing list<br>
                                          <a moz-do-not-send="true"
                                            href="mailto:Rasch@acer.edu.au">Rasch@acer.edu.au</a><br>
                                          Unsubscribe: <a
                                            moz-do-not-send="true"
href="https://mailinglist.acer.edu.au/mailman/options/rasch/thomas.salzberger%40gmail.com"
                                            target="_blank">https://mailinglist.acer.edu.au/mailman/options/rasch/thomas.salzberger%40gmail.com</a><br>
                                        </blockquote>
                                      </div>
                                      <br>
                                      <br clear="all">
                                      <br>
                                      -- <br>
___________________________________<br>
                                      <a moz-do-not-send="true"
                                        href="mailto:Thomas.Salzberger@gmail.com"
                                        target="_blank">Thomas.Salzberger@gmail.com</a><br>
                                      <a moz-do-not-send="true"
                                        href="mailto:Thomas.Salzberger@wu.ac.at"
                                        target="_blank">Thomas.Salzberger@wu.ac.at</a><br>
                                      <br>
                                    </div>
                                  </div>
                                </div>
                              </div>
                            </div>
                          </div>
                        </div>
                      </div>
                    </div>
                  </div>
                </div>
              </div>
            </div>
          </div>
        </div>
      </div>
      <br>
      <fieldset class="mimeAttachmentHeader"></fieldset>
      <br>
      <pre wrap="">_______________________________________________
Rasch mailing list
<a class="moz-txt-link-abbreviated" href="mailto:Rasch@acer.edu.au">Rasch@acer.edu.au</a>
Unsubscribe: <a class="moz-txt-link-freetext" href="https://mailinglist.acer.edu.au/mailman/options/rasch/l.tesio%40auxologico.it">https://mailinglist.acer.edu.au/mailman/options/rasch/l.tesio%40auxologico.it</a></pre>
    </blockquote>
    <br>
    <br>
    <pre class="moz-signature" cols="72">-- 
Luigi Tesio, Professore Ordinario
Cattedra di Medicina Fisica e Riabilitativa
Universitā degli Studi di Milano
Direttore, 
Unitā Clinica e Laboratorio di Ricerche di Riabilitazione Neuromotoria
Ospedale San Luca, Istituto Auxologico Italiano-IRCCS
via Mercalli,32
20122 Milano, Italy
tel +390258218154
fax +390259218152
e.mail : <a class="moz-txt-link-abbreviated" href="mailto:luigi.tesio@unimi.it">luigi.tesio@unimi.it</a>
<a class="moz-txt-link-abbreviated" href="http://www.unimi.it">www.unimi.it</a>
e-mail : <a class="moz-txt-link-abbreviated" href="mailto:l.tesio@auxologico.it">l.tesio@auxologico.it</a>
<a class="moz-txt-link-abbreviated" href="http://www.auxologico.it">www.auxologico.it</a></pre>
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