Paper presented together with Prof. Dr. Richard Bell at the 20th International Conference of Personal Construct Theory (ICPCP), Sydney, July 2013

1. A New Development in the Hierarchical
Clustering of Repertory Grid Data
Mark Heckmann & Richard C. Bell
University of Bremen, Germany, University of Melbourne, Australia
ICPCP, Sydney, July 19, 2013

2. The
Context:
Tight
&
Loose
Construct
Systems
• The
importance
of
the
9ghtness
–
looseness
construct
– Fragmented
vs
Monolithic
construing
dimension
– Involved
in
Kelly’s
Crea9vity
Cycle.
Therapy
involves
a
series
of
Crea9vity
Cycles,
each
of
which
• Starts
with
loosened
construc9on
• Ends
with
9ghtened
construc9on

3. Measuring
9ghtness
and
looseness
• Using
the
Repertory
Grid
• Overall
Grid
9ghtness
&
looseness
of
construing
– Cogni9ve
Complexity
measures
such
as
• Bannister’s
intensity
(Average
correla9on)
• PVAFF
(Percentage
of
Variance
Accounted
for
by
the
First
Factor)
• Number
of
components
• Finding
subsystems
of
9ght
and
loose
construing

4. Measuring
9ghtness
and
looseness
• Using
the
Repertory
Grid
to
find
subsystems
of
9ght
and
loose
construing
• Requires
representa9on
of
rela9onships
between
constructs
that
are
differen9ated
in
terms
of
“closeness”.
– Spa9al
representa9ons
(principal
components)
– Tree
representa9ons
(clustering)
• Neither
readily
permits
objec9ve
iden9fica9on
of
9ght
and
loose
rela9onships

5. Hierarchical
Clustering
of
Grid
Data
• Appears
to
have
originated
with
Thomas
&
Mendoza
in
1974
at
Brunel
University
but
• Made
famous
by
Thomas
&
Shaw
in
1976
as
the
FOCUS
program
– Never
en9rely
clear
which
cluster
method
was
used
–
either
McQuiby
or
Single
Linkage
– Nor
was
the
measure
made
clear
–
probably
city-­‐
block
(Manhaban)
distances
• More
of
an
impact
in
industrial
seengs
than
clinical

6. Hierarchical
Clustering
of
Grid
Data
• Advantage
– Shows
grouping
clearly
• Disadvantages
– Representa9on
(dendrogram)
depends
on
method
of
clustering
and
measure
of
similarity
(between
constructs)
– Can’t
tell
whether
clusters
are
significant
(but
also
true
of
other
representa9ons
such
as
principal
components)

7. Iden9fying
Significant
Clusters
• Recent
advances
in
compu9ng
have
enabled
us
to
assess
significance
without
resor9ng
to
tradi9onal
theore9cal
distribu9ons
such
as
t,
F,
or
z.
• Such
methods
involve
mul9ple
samples
and
include
– Jackknife
(crea9ng
new
samples
using
all
cases
except
(a
different)
one
each
9me)
– Monte
Carlo
(random
data
generated
by
model)
– Bootstrap
(crea9ng
new
samples
by
sampling
with
replacement)

8. SaSarah‘s
grid

9. Prelude:
A
lot
of
grid
sta9s9cs
are
derived
from
similarity
measures
Complexity
(RMS)
Conflic9ng
triads
Implica9ve
Dilemma
Cluster
analysis
Usually
these
sta9s9cs
are
interpreted
‚as-­‐are‘
Correla9ons
Distances
...

10. Standard
hierarchical
cluster
analysis

11. Sar
r
Sarah‘s
grid

12. Some
more
reliability
observa9ons
1. Appr.
70%
of
constructs
remain
the
same1
2. Ra9ngs
of
same
grids
will
vary2
t1
t2
We
get
a
glimpse
but
not
the
whole
picture
à
sampling
from
a
universe
of
constructs
/
elements
1)
Hunt
1951,
Fjeld
&
Landfield
1961
2)
Bell
1990

13. Descriptive Inference
r = 0.35 r ∈ [0.3;0.4]

14. Descriptive Inference
r ∈ [0.3;0.4]
c
c
c
c
c
c
c
c
c
c
c
c
r = 0.35
c
c
c
c
c
c
c
c
c
c
c
c

15. r =.30
Not
feel
guilty
-­‐
Feel
guilty
Powerful-­‐
Powerless
Element
child
self
ommibed
r =.61
Not
feel
guilty
-­‐
Feel
guilty
Powerful-­‐
Powerless
Correla9ons
vary
with
the
element
set
All
elements

16. Element
partner
ommibed
r =.39
à
the
similarity
measure
also
is
a
random
variable
Not
feel
guilty
-­‐
Feel
guilty
Powerful-­‐
Powerless
Idea:
Thinking
of
the
set
of
elements
and
constructs
as
realisia9ons
of
random
variables

17. How
much
does
a
correla9on
vary?
Similarity
measures
may
vary
if
a
different
(sub)set
of
elements
is
used
Safe
to
detect
e.g.
implica9ve
dilemmas
at
r=0.35
no
maber
what?

18. What
about
dendrograms?
No
indica9on
of
associa9on

19. Element
„Child
self“
omibed
Dendrograms
are
based
on
similari9es
and
will
be
affected
by
element
selec9on

20. Assessing
the
stability
of
cluster
solu9ons
• How
can
we
assess
which
parts
of
the
cluster
structure
are
stable?
• Similar
problem
in
phylogene9c
research
• Felstenstein
(1985):
Suggests
Bootstrapping
• Idea:
Resampling
from
the
data
we
have
and
assess
which
structures
remain
stable

21. ①
②
③
Dendrogram
①
AB|CDEF
②
ABCD|EF
③
ABC|DEF
Corresponding
Par33ons
A
B
C
D
E
F

22. A
B
C
D
E
F
A
B
D
C
F
E
A
B
C
E
D
F
AB|CDEF
ABC|DEF
ABCD|EF
AB|CDEF
ABD|CEF
ABCD|EF
BC|ADEF
ABC|DEF
ABCE|DF
Bootstrap
Replicates
Corresponding
Par33ons
AB|CDEF
ABC|DEF
ABCD|EF
AB|CDEF
ABD|CEF
ABCD|EF

23. Par$$on
f
BC|ADEF
1
ABC|DEF
2
ABCD|EF
2
AB|CDEF
2
ABCE|DF
1
ABD|CEF
1
h
BP
.33
33
.67
67
.67
67
.67
67
.33
33
.33
33
A
B
C
D
E
F
Par$$on
f
BC|ADEF
1
ABC|DEF
2
ABCD|EF
2
AB|CDEF
2
ABCE|DF
1
ABD|CEF
1
67
67
67

24. Bootstrap
Probabili9es

25. Approximately
Unbiased

26. AU
and
BP

27. Possible
measures
of
interest:
1. Number
of
(TOP-­‐LEVEL)
significant
clusters
2. Propor9on
of
ALL
constructs
in
significant
clusters
3. Propor9on
of
UNIQUE
constructs
in
significant
clusters

28. What
can
we
make
of
it?
• Do
significant
clusters
indicate
9ghtly
knibed
parts
of
the
construct
system?
• Does
it
have
any
meaning
at
all?
Currently
lack
of
a
valida9on
criterion!

29. Some
similarity
measures
and
cluster
methods
• Manhaban
distance
• Euclidean
distance
• Correla9ons
• ...
• Ward
• Single
linkage
• Complete
linkage
• Average
• McQuiby
• Median
• Centroid
• …
PCP:
FOCUS
procedure
=
Manhaban
distances
plus
Single
linkage.
But
why?

30. Manhaban
Single
linkage

31. Manhaban
Complete
linkage

32. Euclidean
Single
linkage

33. Euclidean
Complete
linkage

38. Conclusions
• Developments
in
other
fields
offer
chances
for
transfer
• Adop9ng
an
inference
view
• No
substan9al
associa9ons
with
global
measures
of
complexity
• Meaning
of
significant
clusters:
subject
to
further
research,
valida9on
or
invalida9on

39. www.onair.openrepgrid.org

40. Thanks !

41. Bell,
R.
(1990).
Repertory
Grid
as
Mental
tests:
Implica9ons
of
test
theories
for
grids.
Journal
of
Construc6vist
Psychology,
3(1),
91-­‐103.
Feixas,
G.,
Saúl,
L.
A.,
&
Sanchez,
V.
(2000).
Detec9on
and
analysis
of
implica9ve
dilemmas:
implica9ons
for
the
therapeu9c
process.
In
J.
W.
Scheer
(Ed.),
The
Person
in
Society:
Challenges
to
a
Construc6vist
Theory.
Giessen:
Psychosozial-­‐Verlag.
Felsenstein,
J.
(1985).
Confidence
Limits
on
Phylogenies:
An
Approach
Using
the
Bootstrap.
Evolu6on,
39(4).
Krauthauser,
H.,
Bassler,
M.,
&
Potratz,
B.
(1994).
A
new
approach
to
the
iden9fica9on
of
cogni9ve
conflicts
in
the
repertory
grid:
A
nomothe9c
study.
Journal
of
Construc6vist
Psychology,
7(4),
283–299.
Slade,
P.
D.,
&
Sheehan,
M.
J.
(1979).
The
measurement
of
“conflict”
in
repertory
grids.
Bri6sh
Journal
of
Psychology,
70(4),
519–524.
Suzuki,
R.,
&
Shimodaira,
H.
(2006).
Pvclust:
an
R
package
for
assessing
the
uncertainty
in
hierarchical
clustering.
Bioinforma6cs
(Oxford,
England),
22(12),
1540–1542.
References