[Rasch] counts to scale conversion

Michael Lamport Commons commons at tiac.net
Wed Jan 25 02:42:43 EST 2006

There seems to be a disconnect here.  Let us say that there is some 
generating mechanism that leads to a scale equation, such as is the case in 
many power law cases.  A Rasch scale will work but it will not take 
advantage of the generator mechanism.  The connection between the generator 
and the outcome scale is crucial.

My Best,

Michael Lamport Commons, Ph.D.
Assistant Clinical Professor
Program in Psychiatry and the Law
Department of Psychiatry
Harvard Medical School
Beth Israel Deaconess Medical Center
234 Huron Avenue
Cambridge, MA 02138-1328

Telephone (617) 497-5270
Facsimile (617) 491-5270
Commons at tiac.net

----- Original Message ----- 
From: "Tim Pelton" <tpelton at uvic.ca>
To: "moritz heene" <moritz.heene at psychologie.uni-heidelberg.de>; "Rasch" 
<Rasch at acer.edu.au>
Sent: Tuesday, January 24, 2006 4:55 AM
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 
accomodate severe misfit.

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

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

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

- 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 
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 
model and report an
erroneous relationship (i.e., tell the crickets how fast to chirp...).



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?

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 
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. 
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 
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 
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
>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.
>Moritz Heene.
>At 10:43 23.01.2006 -0500, you wrote:
>>Content-class: urn:content-classes:message
>>Content-Type: multipart/alternative;
>>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.
>><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.
>>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
>>demonstrates quite nicely the
>>limitations of blindly applying an 'ideal' model. Is it reasonable to 
>>an elegant theoretical model
>>that deviates substantially in it's predictions from the observed data 
>>our lack of understanding of
>>related factors means that we cannot effectively explain such deviations? 
>>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 
>>for other factors?
>>- >===== 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
>>crickets' case).
>> > 2) Any model who permits us to fit the data (the exp(something) looks 
>> > to
>>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 
>>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
>>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 
>>and fail according to a
>>logarithmic spiral, or the growth of populations follows a logistic model,
>>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
>> >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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>> >
>> >
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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
>>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
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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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>Rasch at acer.edu.au

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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