Facet Theory Basic Concepts Erik H' Cohen Bar Ilan University Rome July 2005 3rd International Lab M

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Facet Theory Basic ConceptsErik H. CohenBar
Ilan UniversityRome 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 Concepts The Who
populationWe 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
Regionalization
Rationale
An aspect of the empirical structure
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The various components of the research process
according to Facet Theory (II)
Definitional system for an Universe of
observations
mapping sentence
Regionalization
Rationale
facet role
An aspect of the empirical structure
intercorrelations
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Regionality hypothesisAccording 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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Regionality Theoretical Regionalization (I)

• 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.

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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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What is good manager?
A very simple example of mapping sentence.and
structural verification through SSA and
regionality hypothesis assessment
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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
characteristics of
management as
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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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A New Mapping Sentence
Israeli students consider the
characteristics of
management regarding
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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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The axial model
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
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The modular model
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
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The polar model
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
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What is the meaning of each of these three
geometrical figures?
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The axial model
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
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The modular model
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 a
All the items of element b
All the items of element c
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The polar model
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
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• An axial model example

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The Bloom Taxonomy
Erik H. Cohen University of Bar Ilan,
Israel Rodney A. Clifton University of Manitoba,
Winnipeg, Canada Lance W. Roberts University 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 items
Figure 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 Education
• Published 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 Kahanes
  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. Kahanes 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 ones 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
• 933323311
• 1022222222
• 1112111112
• 1244444223
• 1315252534
• 1432343333
• 1535111123
• 1613121421
• 1722434325
• 1842444444

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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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assesses the effectiveness of the Jewish
educational system delivered within a
Population P
institution,
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which is
to the social environment
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to recipients
by
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using
tools
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for teaching a
aspect of Jewish subject matter
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in relation to time period
concerning
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in order to
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Jewish
in country (M) ?
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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
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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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(No Transcript)
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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

• Biblio and other devices survey

Exploratory mapping sentence
Intercorrelations
SSA representation
Facet analysis
Final mapping sentence
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The research process

• Biblio and other devices survey

Exploratory mapping sentence
Intercorrelations
SSA representation
Facet analysis
Final mapping sentence
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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The Smallest Space Analysis(2)

• 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.

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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)