[Rasch] formative v. reflective measures in assessment research

Thomas Salzberger thomas.salzberger at gmail.com
Sun Oct 27 03:34:00 EST 2013


Don & Luis,

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.

Formative "measurement", or "formative indicators",  is something else. But
Jack has also commented on this (http://www.rasch.org/rmt/rmt221d.htm).

It does not surprise me that many Rasch advocates know very little or
nothing about "formative measurement". And for a good reason.
In my mind, formative measurement is a misconception, a fallacy (see
Edwards: The fallacy of formative measurement, Organizational Research
Methods 2011 vol. 14 no. 2 370-38), and seriously misleading.

Borsboom (2003 The *Theoretical Status of Latent Variables*. 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.

If you critically question Jarvis et al's rules for deciding whether
something has to be measured with reflective indicators (-> factor analysis
in CTT, IRT, Rasch) or formative indicators (-> ? 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.
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.



I was contacted by my agent to make changes in my policy

I was contacted by my agent to sell me more life insurance

I was contacted by my agent to describe new insurance offerings
I was contacted by my agent to keep my policy in place


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?
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.

If I wanted to measure "subjective warmth", I would not use the following
items, would I:

I feel warm because it is hot outside.
I feel warm because the heating is on.
I feel warm because I have a fever.


Best
Thomas




2013/10/26 Luis Carlos Orozco <lcorovar at gmail.com>

> 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.
>
> Luis C. Orozco V. MD MSc
> Profesor Asociado
> Escuela de Enfermería
> Universidad Industrial de Santander
> Colombia
>
>
>
> 2013/10/26 Donald Bacon <dbacon at du.edu>
>
>>  Hi all --****
>>
>> ** **
>>
>> 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 ‘effects indicators’ in a
>> principal component model, and formative indicators ‘causal indicators’ in
>> a composite latent construct model.****
>>
>> ** **
>>
>> Jarvis et al. cite a formative example from Crosby and Stephens (1987)
>> that I will paraphrase here.  In measuring the construct “personal contact
>> with life insurance agents”, suppose the following measures are used:****
>>
>> I was contacted by my agent to make changes in my policy****
>>
>> I was contacted by my agent to sell me more life insurance****
>>
>> I was contacted by my agent to describe new insurance offerings****
>>
>> I was contacted by my agent to keep my policy in place****
>>
>> ** **
>>
>> 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.****
>>
>> ** **
>>
>> 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.  ****
>>
>> ** **
>>
>> 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?****
>>
>> ** **
>>
>> 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? ****
>>
>> ** **
>>
>> Thanks for any insights you may be able to provide.****
>>
>> ** **
>>
>> Don****
>>
>> ** **
>>
>> *From:* rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] *On
>> Behalf Of *Bond, Trevor
>> *Sent:* Saturday, October 26, 2013 1:17 AM
>> *To:* rasch at acer.edu.au
>> *Subject:* Re: [Rasch] formative v. reflective measures in assessment
>> research****
>>
>> ** **
>>
>> Dear Donald,****
>>
>> Perhaps you could share what you mean by formative and reflective, so we
>> might be able better to answer your question.****
>>
>> Collegially****
>>
>> TGB****
>>
>> ** **
>>
>> *From: *Donald Bacon <dbacon at du.edu>
>> *Reply-To: *"rasch at acer.edu.au" <rasch at acer.edu.au>
>> *Date: *Saturday, 26 October 2013 3:57 AM
>> *To: *"rasch at acer.edu.au" <rasch at acer.edu.au>
>> *Subject: *[Rasch] formative v. reflective measures in assessment
>> research****
>>
>> ** **
>>
>> Hi all –****
>>
>>    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’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?****
>>
>>  ****
>>
>> Thanks for any insights you might have –****
>>
>>  ****
>>
>> Don ****
>>
>>  ****
>>
>> Donald R. Bacon, Ph.D.****
>>
>> Professor of Marketing****
>>
>> Editor, Journal of Marketing Education****
>>
>> Daniels College of Business****
>>
>> University of Denver****
>>
>>  ****
>>
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___________________________________
Thomas.Salzberger at gmail.com
Thomas.Salzberger at wu.ac.at
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