Facet Theory Basic
Concepts
Erik H. Cohen
Bar Ilan University
Rome July 2005
3rd International Lab Meeting – Summer session 2005
11th Edition of the International Summer School of the European Ph.D.
1
• 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
2
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
3
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
4
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
5
Facet 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
6
For this purpose, one may use many
methods of sampling :
- Quota method
- Random
- Snowball technique
- etc.
7
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.
8
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.
9
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?
10
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.
11
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).
12
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)
13
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
14
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)
15
The most basic abstract symbolic mapping
sentence has the following format: see Levy
1976
P
{A}

R
Population Content facet  Range
16
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.
17
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.
18
"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)
19
The various components of the research process
according to Facet Theory (I)
Definitional system for an
Universe of observations
Rationale
Regionalization
An aspect of the
empirical structure
20
The various components of the research process
according to Facet Theory (II)
Definitional system for an
Universe of observations
= mapping sentence
Rationale
= facet role
Regionalization
An aspect of the
empirical structure
= intercorrelations
21
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.
22
Regionality hypothesis (2)
A facet with n elements
A map with n regions
With a rationale
23
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.
24
First theoretical regionalization of a Facet with two elements
All the items of
element a
All the items of
element b
25
Second theoretical regionalization of a Facet with two elements
All the items of element a
All the items of
element b
26
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.
27
What is good manager?
A very simple example of mapping
sentence.and structural verification through
SSA and regionality hypothesis assessment
28
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.
29
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.
30
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.
31
A first very simple mapping sentence has the
following format:
32
masculine  characteristics of

Israeli students consider the 

feminine


management as
 almost never true 


to


almost always true 


33
In the facet content, “masculine”
and “feminine” are called facet
elements
34
Our findings
35
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.
36
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.
37
A New Mapping Sentence
masculine  characteristics of

Israeli students consider the 

feminine


management regarding
 himself / herself 


a
manager
in
general


 almost never true 


to


almost always true 


38
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.
39
Findings re to the second facet
40
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”.
41
Conclusion
The interviewees do clearly distinguish
gender characteristics.
The interviewees do not clearly distinguish
between themselves and the good manager.
42
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.
43
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
44
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
45
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
46
What is the meaning of each of these
three geometrical figures?
47
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
48
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 b
All the items of element c
All the items
of element a
49
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
50
An axial model
example
51
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
52
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
53
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.
54
MONCO of the 36 items
55
Legend of the 36 items
56
Second SSA of the 30 items
57
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.
58
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.
59
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
60
The two questions
Is the list of 8 components exhaustive?
Is there redundancy in the list?
61
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
62
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
63
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
64
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933323311
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1244444223
1315252534
1432343333
1535111123
1613121421
1722434325
1842444444
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
65
Basic SSA
66
SSA with lines according to the
theoretical/qualitative criteria
67
An Exploratory Mapping Sentence
for Assessing Jewish Education
Erik H. Cohen
Bar Ilan University
Shlomit Levy
Hebrew University of Jerusalem
68
A


 educator 


 educatee 


Population P  parent 
 manager 


community 


etc
...


assesses the
effectiveness
of the Jewish
educational
system
delivered
within a
 B 
 formal 



 institution,
informal 
 general 
69
which is
 C 


open
close


to the social environment
70
 D 
children 


 youth 
to recipients students 


 adults 


 families 
 general 


by
E


 teacher 


instructor 


counselor 


 Rabbi 
 peer 


 parent 


...


71
using
F


 cognitive 




affective


instrument al
tools
72
 G 
for teaching a specific  aspect of Jewish
subject matter
 general 


H


 religion 


 heritage 


history


 culture 


 society 
unspecifie d 


73
in relation to time
period
J
 I 


 ancient 
 Israel 





 concerning 

modern 
Diaspora 
 general 
 general 
74
in order to
K


 construct 


 improve 
 inspire 


unspecifie d 
75
Jewish
L


commitment 


 identity 


identifica
tion


 involvemen t 


 continuity 
 unspecifie d 


in country (M) 
76
 R 
 low 

 effectiveness in achieving

 specified in facets K-L.
  
high 
educational
goals
77
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).
78
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).
79
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
80
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.
81
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).
82
Israel Experience Programs
mapping sentence:
 satisfaction 
The extent to which participant (P) evaluates his/her 

improvment


 Jewish 
 specific 
 Israeli  character of the educational
with respect to a 
aspect
of
the



general


 general 
 content 
 programs 


high 
 facilities 


domain 
of
his/her
visiting
student
program
in
Israel





staff


 low 


 peer group 


 in general 
evaluation.
83
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)
84
85
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
86
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
87
The Monotonicity
The linear model
The monotone model
88
The research process
Biblio and other devices survey
Exploratory mapping sentence
Intercorrelations
SSA representation
Facet analysis
Final mapping sentence
89
The research process
Biblio and other devices survey
Exploratory mapping sentence
Intercorrelations
SSA representation
Facet analysis
Final mapping sentence
Iterations
90
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.
91
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.
92
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.
93
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.
94
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.
95
Linearity?
The zoology as the science of the nonelephants (Stanislaw Ulam)
96