[Rasch] counts to scale conversion

William Fisher wfisher at avatar-intl.com
Wed Jan 25 02:06:17 EST 2006


This is one of the things that really irritates me in discussions like this. Just because there is a difference of opinion, there is no call for projecting inane opinions on other people. Think it through!!

In the preface (pp. xi-xii) to his classic 1977 book, The Essential Tension, Thomas Kuhn recounts an experience from the summer of 1947 that led to his appreciation for an explicit theory of interpretation (hermeneutics).  He had been completely perplexed by Aristotle's account of motion, in which Aristotle writes a great many things that appear blatantly absurd. Kuhn was very puzzled and disturbed by this, as Aristotle made many astute observations in other areas, such as biology and political behavior. He eventually came to see what Aristotle was in fact talking about, and he then came to routinely offer the following maxim to his students:

"When reading the works of an important thinker [or anyone else who usually seems to have a modicum of coherence], look first for the apparent absurdities in the text and ask yourself how a sensible person could have written them. When you find an answer, I continue, when those passages make sense, then you may find that more central passages, ones you previously thought you understood, have changed their meaning."

As Kuhn goes on to say, if his book was addressed primarily to historians, this point wouldn't be worth making, as historians are in the business of precisely this kind of interpretive back-and-forth. But as a physicist, Kuhn says that the discovery of hermeneutics not only made history seem consequential, it changed his view of science. His skill in practicing hermeneutics changed a great many people's views of science.

So where does Kuhn's maxim lead in the current context? To follow it, we need to keep a fundamental distinction in mind, as described by Roche (1998, p. 231):
  "There is a class of relationship in physics called 'empirical' or 'phenomenological' where the equation which represents it is not dignified by the name 'physical law'. This is usually because it has no known foundation in physical principles, or because its application is very particular. For example, the equation which attempts a best fit to an empirical graph relating thermal expansion of a particular substance to termperature is not thought of as representing a law of physics. The equation itself is then often described as 'modelling' the empirical data."
 
Given that Rasch models have the same mathematical form as physical laws, when data do not fit such a model and are then nonetheless described with an equation, might it be reasonable to suggest that this equation is empirical or phenomenological, that it ought not be dignified with a "lawful" appelation? Might in fact the chirping of crickets have no known foundation in physical, chemical, or biological principles? Might the particularity of crickets' chirping patterns entail a modelling of the empirical data, but not the generalization of a law? 

Might there be some other observational framework, some other way of organizing the crickets' chirps, that might in fact exhibit more lawlike regularities? Is it not conceivable that studying the chirps as though they had some lawlike regularity might lead to the discovery of that regularity more quickly than simply continuing to work within a framework of assumptions informed only by the model of the empirical data? Are not these the basic principles of Rasch measurement taught by Ben Wright to so many? Is sticking to theory so absurd in this light? Might a sensible person be allowed to hold a different opinion without being held to the ridiculous position of "telling the crickets how fast to chirp"? I hope so.

Over and out,
wpf
William P. Fisher, Jr., Ph.D.
AVATAR INTERNATIONAL INC.
WFisher at avatar-intl.com
-----Original Message-----
From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf Of Tim Pelton
Sent: Tuesday, January 24, 2006 4:56 AM
To: moritz heene; Rasch
Subject: RE: [Rasch] counts to scale conversion

Hi again,

I too like good theory.

The example given was of an observed and stable phenomenon.  What benefit 
would there be to forcing 
a fit with a model that may be inadequate.  Certainly theory needs to guide 
scientific process - but 
theory development never occurs in a vacuum.  It is an iterative process 
combining intuitive, qualitative 
and quantitative information as it is acquired and found useful or adjusted to 
accomodate severe misfit.


e.g.
Hmm.. crickets are chirping differently tonight - I wonder why?

Say, yesterday I noticed the pitch was higher than it was today I wonder why?
 - maybe they are hot and are trying to cool down?
- maybe their mating song carries different distances depending on the 
temperature

Let's record and count the chirps and see if they are related to the 
temperature

- wow look at that there seems to be a relationship - but it doesn't seem to 
account for all of the 
deviations... (unless we use a ridiculously complicated curve)

- I think the pitch is even higher after a rain, I wonder if the humidity 
might also be a factor...

Now if we concurrently were examining the nature of relationships between 
insect behavior and their 
environment and we had a theory that all such relationships were linear, we 
might try fitting the data to 
a line and take our observations of poor model data fit as a signal that our 
model theory was not yet 
perfect, or that other factors were still involved.  If we then observed the 
data points and saw a clear 
indication of a parabolic or exponential relationship - would that not justify 
exploration of these 
potential relationships?  If we were explaining what we had discovered  - 
would we not describe it in 
terms of the best fitting of the common trend-lines?

Is anyone suggesting it would be better to simply apply our interim linear fit 
model and report an 
erroneous relationship (i.e., tell the crickets how fast to chirp...).

Tim

---

Here is another article - I haven't had a chance to read it yet though.


Found at: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?
cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=1403993&itool=iconabstr&query_h
l=1&itool=pu
bmed_docsum

J Comp Physiol [A]. 1992 Aug;171(1):79-92.	Related Articles, Links

Temperature coupling in cricket acoustic communication. II. Localization of 
temperature effects on 
song production and recognition networks in Gryllus firmus.

Pires A, Hoy RR.

Kewalo Marine Laboratory, University of Hawaii, Honolulu 96813.

Acoustic communication in Gryllus firmus is temperature-coupled: temperature 
induces parallel 
changes in male calling song temporal pattern, and in female preference for 
song. Temperature effects 
on song production and recognition networks were localized by selectively 
warming head or thorax or 
both head and thorax of intact crickets, then eliciting aggression song 
production (males) or 
phonotaxis to synthetic calling song (females). Because male song is produced 
by a thoracic central 
pattern generator (CPG), and because head ganglia are necessary for female 
song recognition, 
measurements of female phonotaxis under such conditions may be used to test 
the following 
competing hypotheses about organization of the song recognition network: 1. A 
set of neurons 
homologous to the male song CPG exist in the female, and are used as a 
template that determines 
preferred values of song temporal parameters for song pattern recognition (the 
common neural 
elements hypothesis), and 2. temporal pattern preference is determined 
entirely within the head 
ganglia. Neither selective warming of the head nor of the thorax was effective 
in changing female song 
preference, but simultaneous warming of head and thorax shifted preference 
toward a faster song in 
most preparations, as did warming the whole animal by raising ambient 
temperature. These results 
suggest that phonotactic preference for song temporal pattern is 
plurisegmentally determined in field 
crickets. Selective warming experiments during aggression song production in 
males revealed that 
syllable period is influenced but not completely determined by thoracic 
temperature; head temperature 
is irrelevant. The song CPG appears to receive some rate-setting information 
from outside the thoracic 
central nervous system.

>===== Original Message From moritz heene 
<moritz.heene at psychologie.uni-heidelberg.de> 
=====
>Hello to all,
>
>I agree with William Fisher, especially with "Regarding the model as an
>ideal disconnected from reality forgets that the data may be derived from
>questions that may be irrelevant, poorly formulated, or off-construct for
>some other reason, or that some respondents may not belong to the intended
>population."
>So I vote for 3. There is, of course, much to say about theories and formal
>models. But -in my opinion- Guttman hit the nail on the head by stating:
>"Scale analysis has been criticized by some on interesting grounds that it
>does not always 'succeed' like item analysis. Scales don't always exist,
>but people have come to believe that they MUST exist. And some researchers
>are frustrated if they can't construct scores with which to continue to be
>busy." (Psychometrika, 36(4), 1971).
>--> The way I see it: the major advantage of the Rasch model is that it is
>essentially a falsifiable model.
>
>Best,
>
>Moritz Heene.
>
>
>At 10:43 23.01.2006 -0500, you wrote:
>
>>Content-class: urn:content-classes:message
>>Content-Type: multipart/alternative;
>>boundary="----_=_NextPart_001_01C62033.C25DD18B"; 
x-avg-checked=avg-ok-27831F5
>>
>>Regarding the model as an ideal disconnected from reality forgets that the
>>data may be derived from questions that may be irrelevant, poorly
>>formulated, or off-construct for some other reason, or that some
>>respondents may not belong to the intended population.
>>
>>
>>
>>Why try to describe data that are not reproducible and replicable? How
>>well do we understand a construct when the only data we can produce are
>>not theoretically tractable, and so remain tied to particular questions
>>and respondents? It seems pretty cynical to me to do research with the
>>sole aim of applying fancy statistics to data, publishing articles, and
>>advancing ones own career, while deliberately limiting your potential for
>>generalizing your results past your own local samples of persons and items
>>because you choose models and methods that do not push you toward the
>>highest possible level of generality.
>>
>>
>>
>>I vote for 3. Strong construct theory is not automatically implied by
>>strong measurement theory. Being able to predict item difficulties when
>>the items have been previously calibrated is great, but the real goal is
>>to be able to predict their calibrations on the basis of their theoretical
>>properties, in the manner of Lexiles or Commonsstage scoring system.
>>
>>
>>
>>When we have this, then were getting somewhere. After all, imagine how
>>different our economic lives would be if rulers, weight scales,
>>thermometers, clocks, volt meters, and the resistance properties of every
>>meter of every type of electrical cable all had to be calibrated
>>individually on data, instead of en masse, by theory&.  Theoretical
>>predictability is the mark of a real science, where we understand a
>>variable to the point that we can recognize it for what it is in any
>>amount when we see it.
>>
>>
>>
>>After all, dont we say that a basic mark of knowing what were talking
>>about is being able to put it in our own words? Shouldnt any valid
>>articulation of a construct be a viable medium for measuring in a
>>univerally uniform reference standard metric?
>>
>>
>>
>>Jack Stenner has recently done some work describing several more than
>>three stages of this kind in the development of measurable
>>constructs&.  Maybe we can get him to weigh in&.
>>
>>
>>
>>William P. Fisher, Jr., Ph.D.
>>AVATAR INTERNATIONAL INC.
>><mailto:WFisher at avatar-intl.com>WFisher at avatar-intl.com
>>
>>----------
>>From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On
>>Behalf Of Agustin Tristan
>>Sent: Monday, January 23, 2006 10:26 AM
>>To: Tim Pelton; Rasch at acer.edu.au
>>Subject: RE: [Rasch] counts to scale conversion
>>
>>
>>
>>Hi Tim...it could be nice to have further votes for the three options and
>>see how well this example fits to the person's opinion in this
>>listserve... or how well our opinions fit a model...
>>
>>Thank you.
>>
>>Agustin
>>
>>Tim Pelton <tpelton at uvic.ca> wrote:
>>
>>What a great example - and starting point for a discussion...
>>
>>My vote is for option 2.
>>
>>I think that the phrase in option 3 "...telling us (and the crickets 
too)..."
>>demonstrates quite nicely the
>>limitations of blindly applying an 'ideal' model. Is it reasonable to favor
>>an elegant theoretical model
>>that deviates substantially in it's predictions from the observed data when
>>our lack of understanding of
>>related factors means that we cannot effectively explain such deviations? Is
>>it not more appropriate to
>>choose a pragmatic model (balancing simplicity and accuracy) as an
>>intermediate model to help us
>>establish a control or baseline which may then be used to support our search
>>for other factors?
>>
>>Tim
>>
>>
>>- >===== Original Message From Agustin Tristan =====
>> >Hi! I'm trying to follow this topic concerning crickets and scales.
>> > In abstract: Which is better?
>> > 1) The simple linear model even if it doesn't fit (the linear model for 
the
>>crickets' case).
>> > 2) Any model who permits us to fit the data (the exp(something) looks to 
be
>>like that).
>> > 3) A theoretical model telling us (and the crickets too) how is the way
>>crickets should adjust the
>>frequency of the noise they produce according to temperature...specially if
>>this theoretical model is
>>exp(someting) because it looks more interesting or impressive.
>> >
>> > I like Nature and its relationship with math and for me it was 
interesting
>>to know that crickets may
>>use the exponential (even if they don't care about the mathematical
>>formulation), as well as the seeds in
>>sunflowers grow exponentially from their center, or the snails grow their
>>shell, or the ivy plants grow in
>>an helical 3D curve, or the soil slopes (in soil mechanics) become unstable
>>and fail according to a
>>logarithmic spiral, or the growth of populations follows a logistic model, 
and
>>so forth... I can also
>>recognize that I prefer objective items that behave as the Rasch model,
>>but...I cannot decide in all those
>>case which is better between (1), (2) and (3)...
>> > Regards
>> > Agustin Tristan
>> >
>> >Rense wrote:
>> >
>> >All this illustrates that if we want to stay in business as test gurus 
then
>> >we'd better forget about meaningful item hierarchies, sample independence,
>> >additive measures, and other such niceties. Rather, using methods whose
>> >results need to be recalibrated for boys, girls, old, and young, ..,
>> >whatever, ... - and adding a few things like "log(exp(something ...))" to
>> >our tech reports - should greatly help with job security. :)
>> >
>> >Rense Lange
>> >
>> >-----Original Message-----
>> >From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au]On
>> >Behalf Of Trevor Bond
>> >Sent: Saturday, January 21, 2006 5:43 PM
>> >To: Rasch listserve
>> >Subject: [Rasch] counts to scale conversion
>> >
>> >
>> >For all budding scale constructors, this is a hoot:
>> >http://www.dartmouth.edu/~genchem/0102/spring/6winn/cricket.html
>> >check the lovely graphs
>> >collegially
>> >Trevor
>> >--
>> >Trevor G BOND Ph D
>> >Professor and Head of Dept
>> >Educational Psychology, Counselling & Learning Needs
>> >D2-2F-01A EPCL Dept.
>> >Hong Kong Institute of Education
>> >10 Lo Ping Rd, Tai Po
>> >New Territories HONG KONG
>> >
>> >Voice: (852) 2948 8473
>> >Fax: (852) 2948 7983
>> >Mob:
>> >
>> >_______________________________________________
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>> >
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>> >
>> >
>> >FAMILIA DE PROGRAMAS KALT.
>> >Mariano Jiménez 1830 A
>> >Col. Balcones del Valle
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>>Tim Pelton
>>Assistant Professor
>>Department of Curriculum and Instruction
>>University of Victoria
>>PO Box 3010 STN CSC
>>Victoria BC V8W 3N4
>>Phone: (250)721-7803
>>Fax (250) 721-7598
>>
>>
>>
>>FAMILIA DE PROGRAMAS KALT.
>>
>>Mariano Jiménez 1830 A
>>
>>Col. Balcones del Valle
>>
>>78280, San Luis Potosí, S.L.P. México
>>
>>TEL (52) 44-4820 37 88, 44-4820 04 31
>>
>>FAX (52) 44-4815 48 48
>>
>>web page (in Spanish AND ENGLISH): http://www.ieesa-kalt.com
>>
>>
>>What are the most popular cars? Find out at
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>
>Dipl.-Psych Moritz Heene
>AE Differentielle Psychologie und Psychologische Diagnostik
>Psychologisches Institut
>Universität Heidelberg
>Hauptstr. 47-51
>D-69117 Heidelberg
>
>Tel.: +49 (0)6221-54 7281
>
>
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Tim Pelton
Assistant Professor
Department of Curriculum and Instruction
University of Victoria
PO Box 3010 STN CSC
Victoria  BC V8W 3N4
Phone: (250)721-7803
Fax (250) 721-7598

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