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Facet Theory Basic Facet Theory Basic ConceptsConcepts

Erik H. CohenBar Ilan University

Rome July 2005 3rd International Lab Meeting – Summer session 2005

11th Edition of the International Summer School of the European Ph.D.

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• Submit a small matrix to convert in hand SSA, according to two rules: inverse and direct

• Submit a small number of profiles to be transformed by hand in POSAC

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Table of Contents

The Who Population

The What Population

The Concept of Mapping Sentence

What is a Facet?

The Range

Definition of theory by Guttman

The various components of the research process according to Facet Theory

Regionality hypothesis

Theoretical Regionalization (I)

What is the meaning of each geometrical figure?

What is good manager?

Our findings

Interpretation

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Extension of the research

A new mapping sentence

Hypothesis

The Findings relating to the second facet

Interpretation

Conclusion

Theoretical Regionalization (II) 

The axial model 

The modular model 

The polar model 

What is the meaning of each of these three geometrical figures? 

The axial model 

The modular model 

The polar model

 

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An Exploratory Mapping Sentence for Assessing Jewish Education 

Factorial design (R.A. Fisher) 

Cumulative Knowledge 

Another example 

Israel Experience Programs mapping sentence

The Monotonicity

The research process

The Smallest Space Analysis (I, II, III)

Bibliography

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Facet Theory Basic ConceptsFacet Theory Basic Concepts

The Who population

We know how to cover a population in such a way that the surveyed sample represents the

referenced population.

p represents P

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For this purpose, one may use many methods of sampling :

- Quota method

- Random

- Snowball technique

- etc.

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According to certain rules, we may be even capable of estimating the degree of error in the sampling.

For example : + or – 2,5% is a quite good such estimate for surveys in elections.

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The population may be everything in the world:

people of a certain country,

trees of a forest,

articles published in international conferences,

stamps of a certain year / country / language, etc.

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The What population

But there is another kind of population, which is generally less systematically analyzed: the population / universe of contents.

How can we know - as we can do it in the Who population - that the survey will represent the What population? What kind of tool could help us in this aim?

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The bibliography literature survey is obviously the first thing to do.

A state of the art survey is surely helpful. It may even lead to discover uncovered issues in the

research.

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The Concept of Mapping Sentence 

As Louis Guttman claims : “the problem of proposing fruitful facets to the design of the content for a system of variables has generally been found to be a far more difficult one than for that of proposing background variables or experimental conditions for populations” (Guttman, 1992 in Levy 1994).

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In order to allow a systematic design of a field under investigation, Guttman introduced the concept of a mapping sentence. A mapping sentence, which is a basic device of facet theory, contains a variety of facets. Each facet is one way of classifying the research content.

(Guttman 1982)

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What is a Facet?

A facet is one way of classifying the research content .

Each facet contains elements.

It is a set with a rule

in such a way that its elements are both exclusive and exhaustive

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The Range

When we survey a field, any field, we apply some range in our observation.

In esthetic judgment, we refer to the extent of beauty in some object.

What may define an item as value, is its range from “important” to “not important”.

(See Levy 1985 in Canter)

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The most basic abstract symbolic mapping sentence has the following format: see Levy 1976 

P {A} R 

Population Content facet Range

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Though the mapping sentence introduces formality, it is a flexible device as it can easily, but systematically, be enlarged or condensed by adding or reducing facets or elements within the facets.

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Definition of theory by Guttman

As some basic concepts are now understood, we may approach the definition of Theory. This definition will transform these concepts into an operational and integrative process of research.

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A theory is an hypothesis of a correspondence " between a definitional system for a universe of observations and an aspect of the empirical structure of those observations, together with

a rationale for such an hypotheses"

)Guttman 1973, 1982; in Levy 1994(

 

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The various components of the research process according to Facet Theory (I)

Definitional system for an Universe of observations

An aspect of the empirical structure

Rationale Regionalization

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The various components of the research process according to Facet Theory (II)

Definitional system for an Universe of observations

An aspect of the empirical structure

Rationale Regionalization

=mapping sentence

=facet role

=intercorrelations

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Regionality hypothesis

According to the regionality hypothesis, to each element of the facet considered, there will be a specific and continuous region in a geometric representation of

the various items analyzed. There will be a distinction among the various items according to the facet definition of each

item. 

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Regionality hypothesis (2)

A facet with n elements

A map with n regions

With a rationale

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Let first consider the smallest facet existing, i.e. a facet with only 2 ordered elements. This facet may be represented in two and

only two different geometric ways, according to the regionality hypothesis.

Regionality Theoretical Regionalization (I)

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First theoretical regionalization of a Facet with two elements

All the items of

element a

All the items of

element b

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Second theoretical regionalization of a Facet with two elements

All the items of element a

All the items of

element b

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What is the meaning of each geometrical figure?

In the first one, the two elements have an equal role / status

In the second one, the two elements have a different role / status .

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A very simple example of mapping sentence.and structural verification through SSA and regionality hypothesis assessment

What is good manager?

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In their work, “The ‘good manager’: masculine or androgynous” (1979), Powell and Butterfield were the first researchers to specifically apply the concept of androgyny to the work setting.

Based on findings in non-organizational settings, they hypothesized that the “good manager” would be perceived as androgynous in sex-role identification.

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This hypothesis was not supported; both male and female business students described a good manager most of all in masculine terms and least of all in feminine terms. A study, twenty years later (Cohen & Bloom 2000), re-explores the same research questions.

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79 Israeli students completed the Bem Sex Role Inventory (BSRI) (Bem, 1974), a standard tool for measuring femininity, masculinity, and androgyny, both for him/herself and for a good manager.

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A first very simple mapping sentence has the following format:

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Israeli students consider the

feminine

masculine characteristics of

management as

truealwaysalmost

to

never truealmost

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In the facet content, “masculine” and “feminine” are called facet

elements

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Our findings

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Interpretation

The previous geometric representation of the intercorrelations between the 80 various items

shows clearly (there is only one “error”) that the respondents distinguish between male and female

characteristics of the good manager .The regions corresponding to the two elements of the Facet are specific and contiguous, without a

“mixed” region .

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Extension of the research

As we already said, the mapping sentence is a formal but flexible way to formulate the content of a

domain.Now that we have established a first Facet, we may be conducted to enlarge the mapping sentence by a new

Facet.As the respondents were asked to designate the

characteristics of a good manager in general, but also if they consider themselves as fitting these characteristics, we can add a new Facet, which formulates the person targeted by the definition.

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Israeli students consider the

feminine

masculine characteristics of

management regarding

generalin manager a

herself / himself

truealwaysalmost

to

never truealmost

A New Mapping Sentence

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Hypothesis

As the first Facet, the new Facet includes only 2 elements .

We may expect a modular geometric representation, with the himself/herself

items in the center.

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Findings re to the second facet

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Interpretation

The previous geometric representation of the intercorrelations between the various items

shows that the respondents DO NOT distinguish between himself/herself characteristics and the

characteristics of a good manager in general .There are not regions corresponding to the two

elements of the Facet!The various items belonging to the two elements of

the new Facet are “mixed .”

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Conclusion

The interviewees do clearly distinguish gender characteristics.

The interviewees do not clearly distinguish between themselves and the good manager.

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Theoretical Regionalization (II)

Let now consider a more complex facet, i.e. a facet with 3 elements. This facet may be represented in

three and only three different geometric ways, according to the regionality hypothesis.

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First theoretical regionalization of a Facet with three elements

All the items of

element a

All the items of

element b

All the items of

element c

The axial model

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Second theoretical regionalization of a Facet with three elements

All the items of element a

All the items of

element b

All the items of element c

The modular model

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Third theoretical regionalization of a Facet with three elements

All the items of element a

All the items of

element b

All the items of element c

The polar model

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What is the meaning of each of these three geometrical figures?

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The three elements are ranged. For instance, from simple to complex (for instance the Bloom taxonomy is expected this model: Cohen,

Clifton & Roberts 2001)

All the items of

element a

All the items of

element b

All the items of

element c

The axial model

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The three elements have a different role / status, from a core to the

periphery.For instance the intelligence tests analysis shows such a structure, with from

the core to the periphery: inference, application, learning Guttman Levy 1991

All the items

of element aAll the items of

element b

All the items of element c

The modular model

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The three elements have a partially range format. The life areas appear in such a way (Levy Guttman 1975 Cohen 2000).

All the items of element a

All the items of

element b

All the items of element c

The polar model

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An axial model example

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The Bloom Taxonomy

Erik H. CohenUniversity of Bar Ilan, Israel

Rodney A. CliftonUniversity of Manitoba, Winnipeg, Canada

Lance W. RobertsUniversity of Manitoba, Winnipeg, Canada

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Previous FA results

Clifton, Etcheverry, Hasinoff and Roberts (1996) extracted and identified two dimensions in the cognitive domain, even though they constructed the scale items to include all six of the dimensions in Bloom's taxonomy. The two dimensions that emerged included a Structural dimension and a Functional dimension

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First SSA of the 36 itemsFigure 1: Smallest Space Analysis (SSA) of the 36 Items Based on the Pearson Coefficients Matrix Space Diagram for Dimensionality 4. Axis 1 versus Axis 2.

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MONCO of the 36 items

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Legend of the 36 items

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Second SSA of the 30 items

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An example of exploratory Guttman approach:

A Structural Analysis of the Reuven Kahane Code of Informality: Elements Toward a Theory of Informal

EducationPublished in

Sociological Inquiry. 2001, Vol. 71, No. 3, Summer, 357-380.

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1975-1997

After years of reflection and deliberation, Kahane concluded that there are eight structural components of informality.

These are: voluntarism, multiplexity, symmetry, dualism, moratorium, modularity, expressive instrumentalism, and symbolic pragmatism.

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These structural components have not remained constant or consistent throughout Kahane’s career, with both their number and their definitions undergoing modifications over the years

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The two questions

Is the list of 8 components exhaustive?

Is there redundancy in the list?

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R. Kahane’s articles

• Structures and Uses of Informal Organizations 1974

• Informal Youth Organizations: A General Model 1975

• Informal Socialization 1988• Multi-code Organizations 1988• Tutorial Relations Agencies 1989• Origins of Post-modern Youth 1997

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Origins of Post-modern Youth 1997 (1)

• Voluntarism a relatively constraint-free pattern of choice (of goals, means, affiliations,) in which the cost of changing one’s mind is minimal

• Multiplicity/multiplexity a wide spectrum of activities that are more or less equivalent in value

• Symmetry a balanced reciprocal equivalence of principles and expectations in which no party can impose his or her will on another

• Dualism the simultaneous existence of different orientations such as ascription and achievement, competition and cooperation

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Origins of Post-modern Youth 1997 (2)

• Moratorium a temporary delay of duties and decisions that allows for trial and error within wide institutional boundaries

• Modularity eclectic construction of activity sets according to changing interest and circumstances

• Expressive instrumentalism/active expressiveness a combination of activities that are performed both for their own sake and as a means of achieving future goals

• Symbolic pragmatism/pragmatic symbolism the attribution of symbolic significance to deeds and/or the conversion of symbols into deeds

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The data set The observations

1 'tsofe' 2 'wsy' 3 'social' 4 'bne'

5 'tsofe2' 6 'wsy2' 7 'social2' 8 'bne2' 9 'wand' 10 'scout' 11 'komso' 12 'excur' 13 'camp' 14 'polit' 15 'cultur' _ 16 'sport' 17 'intell' 18 'game'

The variables vol mul sym dua mor mod exp pra

143212242 243433333 324432234 423224323 542333221 642332222 744444432 811111113 933323311102222222211121111121244444223131525253414323433331535111123161312142117224343251842444444

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Basic SSA

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SSA with lines according to the theoretical/qualitative criteria

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An Exploratory Mapping Sentence for Assessing Jewish Education

Erik H. Cohen Shlomit Levy

Bar Ilan University Hebrew University of Jerusalem

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...etc

community

manager

parent

educatee

educator

A

Population P

assesses the effectiveness of the Jewish educational system delivered within a

general

informal

formal

B

institution ,

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close

open

C which is to the social environment

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to recipients

general

families

adults

students

youth

children

D

by

...

parent

peer

Rabbi

counselor

instructor

teacher

E

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using

alinstrument

affective

cognitive

F

tools

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for teaching a

general

specific

Gaspect of Jewish subject matter

dunspecifie

society

culture

history

heritage

religion

H

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in relation to time period

general

modern

ancient

I

concerning

general

Diaspora

Israel

J

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in order to

dunspecifie

inspire

improve

construct

K

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Jewish

dunspecifie

continuity

tinvolvemen

tionidentifica

identity

commitment

L

in country (M)

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high

low

R

effectiveness in achieving educational goals specified in facets K-L.

 

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Factorial design (R.A. Fisher)

The 11 various content facets can generate no less than 1,679,616 various sentences (as combinations of their various elements). And this is even not the total number as the facet R has also to be considered (after Guttman 1992 in Levy 1994).

 

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Carrying out such a total design is generally impossible in practice, and, ways are

sought in each case in practice to make only a small sample of observations that

will nevertheless suffice to yield essential information desired about the facet.

)after Guttman 1992.(

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The facets of a given design are generally but a sample from a much larger set of

possible facets, and some selection rule is needed for them

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Cumulative Knowledge

Using a device such as the mapping sentence and Guttman methods such Smallest Space Analysis, the various researchers in a certain field of research may launch a process of an international cumulative knowledge process.

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Another example

In the next slides, we will present another study conducted among participants in summer and winter educational programs for Jewish youth from Diaspora during the last years (Cohen 1995).

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Israel Experience Programs mapping sentence:

.evaluation

Israel in program studentvisiting his/her of domain

leducationathe of character the of aspect a to respect with

his/her evaluates (P) tparticipan whichto extentThe

low

high

in general

peer group

staff

facilities

programs

content

general

Israeli

Jewish

general

specific

improvment

onsatisfacti

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In the following slide, appears the geometrical representation of correlation matrix of the 41

variables of the survey as designed following the previous mapping sentence.

Two main geometric shapes appear: a polar one

(corresponding to the Facet “domain”) and a modular one

(corresponding to the “specific / general” Facet)

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The Linear Model

The linear model • There is only one way to get the peak of the mountain

• The distance from one point to another one must be equal in x and y

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The Monotonicity

• There are many ways to get the peak of the mountain

• The distance from one point to another one must not be equal in x and y. In other terms, when x grows, the only request is that y does not regress.

The monotone model

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The Monotonicity

The linear model The monotone model

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The research process

Intercorrelations

Biblio and other devices survey

Exploratory mapping sentence

Final mapping sentence

SSA representation

Facet analysis

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The research process

Intercorrelations

Biblio and other devices survey

Exploratory mapping sentence

Final mapping sentence

SSA representation

Facet analysis

Iterations

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The Smallest Space Analysis (1)

Based on a correlation matrix, points representing the variables are plotted on a cognitive “map” revealing distinct regions of correlated data (Guttman, 1968, 1982; Levy, 1994) .

By definition, a structure can be found for any data in n-1 dimensions, where n equals the number of items in the correlation matrix .

Therefore, the smaller the number of dimensions necessary to discern a structure, the stronger the significance and credibility of the findings .

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SSA analyzes a matrix of correlations between items by graphically representing them as points

in a Euclidean space called the "smallest space ".

The points are plotted according to the principle: the higher the correlation between two items, the closer they are on the map and, conversely, the lower the correlation, the further apart they are.

The Smallest Space Analysis(2)

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The Smallest Space Analysis(3)

The regionality in an SSA map is defined semantically and not in terms of pure proximity.

The region is not necessarily a cluster.

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Bibliography (1)Bem, S.L. (1974). The Measurement of Psychological Androgyny. Journal of Consulting and Clinical Psychology, 42,

155-162.

Cohen, E.H. (1995). Toward a Strategy of Excellence, A Systemic Analysis and Policy Research Based on External Variables in SSA. In Facet Theory Analysis and Design (J.J. Hox, G.J. Mellenbergh, P.G. Swanborn, Eds.), University of Amsterdam, 55-62.

 Cohen, E.H. (2000). A facet theory approach to examining overall and life facet satisfaction relationships. Social

Indicators Research, Vol. 51, No. 2, 223-237.  Cohen, E. H., R. A. Clifton and L. W. Roberts (2001). The Cognitive Domain of the Quality of Life of University

Students: A Re-analysis of an instrument. Social Indicators Research, Vol. 53, 63-77. Guttman, L. (1968). A General Nonmetric Technique for Finding the Smallest Coordinate Space for a Configuration of

Points, Psychometrika, 33, pp. 469-506.

Guttman, L. (1973). Quoted in Gratch, H. (ed.). Twenty-Five Years of Social Research in Israel. Jerusalem: Jerusalem Academic Press.

 Cohen, Erik H and Naomi Bloom (2000). Evaluating the “Good Manager” and the Self According to the BEM Sex Role

Inventory, in Work Values and Organizational Behavior Toward the New Millennium, Jerusalem. Pp. 77-82.

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Bibliography (2)

Guttman, L and Levy, S. (1975). On the Mutlivariate Structure of Wellbeing, Social Indicators Research, 2, pp. 361-388.

Guttman, L (1992). The Mappimg Sentence for Assessing Values, in Levy, S. (1994). Louis Guttman on Theory and Methodology: Selected Writings. NH: Dartmouth U.

Guttman, L and Levy, S. (1991). Two Structural Laws for Intelligence Tests, Intelligence, 15, pp. 79-103.

Levy, S. (ed.) (1994). Louis Guttman on Theory and Methodology: Selected Writings. NH: Dartmouth U.

 

Levy, S. and L. Guttman (1975). On the multivariate structure of well-being. Social Indicators Research 2, 361-388

Levy, S. (1985). Lawful Roles of Facets in Social Theories, in Canter, D. Facet Theory: Approaches to Social Research, New York: Springer-Verlag..

 

Powell, G.N. and Butterfield, D.A. (1979). The “Good Manager”: Masculine or Androgynous? Academy of Management Journal, 22, 395-403 .

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Linearity?

The zoology as the science of the non-elephants (Stanislaw Ulam)