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