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Presentation on metaphor and measurement given in invited symposium on validity in measurement, International Meetings of the Psychometric Society, July 2012
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Metaphor as Measurement and Vice Versa
A Study of the Metaphor“Love is a Rose”
William P. Fisher, Jr.University of California, Berkeley
International Meeting of the Psychometric Society
9-13 July 2012Lincoln, Nebraska
Two Preliminary Points
• On the distinction between the literal and the metaphorical…
• Metaphor is necessary in discourse as it is the means by which new things come into language.
Overview
• Metaphors as construct models• Models as construct metaphors• A study of “Love is a rose”• Implications• Directions for future research
"What I cannot create, I do not understand."
From Richard Feynman's Caltech classroom blackboard at the time of his death.
Hawking, S. W. (2001). The universe in a nutshell. New York: Bantam Books, p. 83.
Constructs Recreated from Theory
• Irvine, Dunn, Anderson, 1990– British Army Recruitment Battery R > .70
• Embretson, 1998: Abstract Reasoning Test R > .70• Stenner & Smith, 1982: Knox Cube Test R > .90• Fischer, 1973: Elementary calculus test R > .85• Stenner, et al, 1983: Peabody Vocab Test R > .80• Stenner, et al, 1997: Reading tests R > .90• Bejar, et al, 2003: Math tests R > .85• Fisher, 2008: Physical function surveys R > .90
Criteria for Laboratory Synthesis and Demonstrated Understanding
• Data fit a model has the form of a multiplicative scientific law.
• A linear unit is defined by the invariance of the estimates across subsamples.
• A predictive theory explains a significant portion of the variance in the item location estimates.
• The metaphor-model informs a distributed metrology system for point-of-use applications.
"Every metaphor is the tip of a submerged model." Black, M. (1962). Models and metaphors.
Ithaca, New York: Cornell University Press, p. 30.
And so might it also be that every model elaborates an often unnoticed metaphor?
Perhaps there would be some value in expanded use of a concept of heuristic fiction, fictional
truth, or guiding ideal.
Models as Metaphors
“To take a parallel from elementary physics:
A ‘mathematical pendulum’ is defined as ‘a
heavy point, swinging frictionless on a
weightless string in vacuum.’ A contraption like
that was never seen; thus as a model for the
motion of a real pendulum it is ‘unrealistic’. “Rasch (1973/2011, p. 1309)
• George Box (1979, p. 202):– “All models are wrong, but some are useful.”
• Georg Rasch (1960, pp. 37-38):– “That the model is not true is certainly correct, no
models are—not even the Newtonian laws…. Models should not be true, but it is important that they are applicable.”
• Also see Rasch (1973/2011):– “All statistical models are wrong!”
Models as Metaphors
“Love is a rose”
Love is a Rose Study
• 68 entailments, such as– Love is beautiful. Love is thorny.– Love can be bought in a store.– Love grows in the ground.– Love is given to a special person.– Love fades. Love needs sunlight.– Love has leaves. Love inspires passion.
• Before data were gathered, entailments were divided into three groups• Most likely to be rated TRUE• Rating UNDECIDABLE• Most likely to be rated UNTRUE
Construct Hypotheses
Three survey forms
• 33-36 items each– 20 items in common– 11-14 items unique to each form
• On each form, items were selected to– Span the full expected calibration range– Represent equally the three
hypothetical groups
36 total respondents• Subset of original 44– Selected for completion & cooperative
responses– Locations• 15 in Moline, Illinois• 21 in Chicago, Illinois
– Sex• 18 Female• 18 Male
– Age• Overall average 39.2• No significant differences by location or sex
Model-MetaphorMultiplicative Form of Rasch Rating Scale Model
Lrqs = Or / Vq / Es
where• L is the rate at which love is a rose in the
interaction of person r with entailment q at the s level of fictional truth, and L is equal to• the love-rose experience O of person r divided by • the love-rose unity V of entailment q and divided
by• the level of love-rose fictional truth E of rating s.
Persons
Entailments
15-20 responses per item.
R = .94R disattenuated = 1.00
17 or 18 responses per item for each group.
35 or 36 responses per item.
F = .08, 3 df, p = .97
Romantic entailments of “love is a rose.”
Concrete entailments of “Love is a rose”
Conclusions
• The model has the form of a multiplicative scientific law.
• A linear unit is defined by the invariance of the estimates across subsamples.
• A predictive theory explains about 80% of the variance in the item location estimates.
• The metaphor itself embodies a distributed metrology system for point-of-use expressions of a measure of romantic love.
"The greatest thing by far is to be a master of metaphor.”
Aristotle