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A New Development in the Hierarchical
Clustering of Repertory Grid Data
Mark Heckmann & Richard C. Bell
University of Brem...
The	
  Context:	
  Tight	
  &	
  Loose	
  Construct	
  
Systems	
  
•  The	
  importance	
  of	
  the	
  9ghtness	
  –	
  ...
Measuring	
  9ghtness	
  and	
  looseness	
  
•  Using	
  the	
  Repertory	
  Grid	
  
•  Overall	
  Grid	
  9ghtness	
  &...
Measuring	
  9ghtness	
  and	
  looseness	
  
•  Using	
  the	
  Repertory	
  Grid	
  to	
  find	
  subsystems	
  
of	
  9g...
Hierarchical	
  Clustering	
  of	
  Grid	
  Data	
  
•  Appears	
  to	
  have	
  originated	
  with	
  Thomas	
  &	
  
Men...
Hierarchical	
  Clustering	
  of	
  Grid	
  Data	
  
•  Advantage	
  
– Shows	
  grouping	
  clearly	
  	
  
•  Disadvanta...
Iden9fying	
  Significant	
  Clusters	
  
•  Recent	
  advances	
  in	
  compu9ng	
  have	
  enabled	
  us	
  
to	
  assess...
SaSarah‘s	
  grid	
  
Prelude:	
  A	
  lot	
  of	
  grid	
  sta9s9cs	
  are	
  
derived	
  from	
  similarity	
  measures	
  
	
  
Complexity	
 ...
Standard	
  hierarchical	
  cluster	
  analysis	
  
Sar
r
Sarah‘s	
  grid	
  
Some	
  more	
  reliability	
  observa9ons	
  
1.  Appr.	
  70%	
  of	
  
constructs	
  remain	
  
the	
  same1	
  
2.  Ra...
Descriptive Inference
r = 0.35 r ∈ [0.3;0.4]
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
r =.30
Not	
  feel	
  guilty	
  -­‐	
  Feel	
  guilty	
  
Powerful-­‐	
  Powerless	
  
Element	
  child	
  self	
  ommibed...
Element	
  partner	
  ommibed	
  
r =.39
à	
  the	
  similarity	
  measure	
  also	
  is	
  a	
  random	
  variable	
  
N...
How	
  much	
  does	
  a	
  correla9on	
  vary?	
  
Similarity	
  measures	
  
may	
  vary	
  if	
  a	
  different	
  
(sub...
What	
  about	
  dendrograms?	
  
No	
  indica9on	
  
of	
  associa9on	
  
Element	
  „Child	
  self“	
  omibed	
  	
  
Dendrograms	
  
are	
  based	
  on	
  
similari9es	
  and	
  
will	
  be	
  a...
Assessing	
  the	
  stability	
  of	
  
cluster	
  solu9ons	
  
•  How	
  can	
  we	
  assess	
  which	
  parts	
  
of	
  ...
①	
   ②	
  
③	
  
Dendrogram	
  
①	
  AB|CDEF	
  
②	
  ABCD|EF	
  
③	
  ABC|DEF	
  
Corresponding	
  
Par33ons	
  
A	
   B...
A	
   B	
   C	
   D	
   E	
   F	
   A	
   B	
   D	
   C	
   F	
   E	
   A	
   B	
   C	
   E	
   D	
   F	
  
AB|CDEF	
  
AB...
Par$$on	
  	
  	
  	
  f	
  
BC|ADEF	
  	
  	
  1	
  
ABC|DEF	
  	
  	
  2	
  
ABCD|EF	
  	
  	
  2	
  
AB|CDEF	
  	
  	
 ...
Bootstrap	
  Probabili9es	
  	
  
Approximately	
  Unbiased	
  
AU	
  and	
  BP	
  
Possible	
  measures	
  of	
  interest:	
  
1. Number	
  of	
  (TOP-­‐LEVEL)	
  significant	
  clusters	
  
2. Propor9on	
 ...
What	
  can	
  we	
  make	
  of	
  it?	
  
•  Do	
  significant	
  clusters	
  indicate	
  9ghtly	
  knibed	
  
parts	
  of...
Some	
  similarity	
  measures	
  and	
  
cluster	
  methods	
  
•  Manhaban	
  distance	
  
•  Euclidean	
  distance	
  
...
Manhaban	
  
Single	
  linkage	
  
Manhaban	
  
Complete	
  	
  linkage	
  
Euclidean	
  
Single	
  linkage	
  
Euclidean	
  
Complete	
  linkage	
  
Conclusions	
  
•  Developments	
  in	
  other	
  fields	
  offer	
  
chances	
  for	
  transfer	
  
•  Adop9ng	
  an	
  inf...
www.onair.openrepgrid.org
Thanks !
Bell,	
  R.	
  (1990).	
  Repertory	
  Grid	
  as	
  Mental	
  tests:	
  Implica9ons	
  of	
  test	
  theories	
  
for	
  ...
A new development in the hierarchical clustering of repertory grid data
A new development in the hierarchical clustering of repertory grid data
A new development in the hierarchical clustering of repertory grid data
A new development in the hierarchical clustering of repertory grid data
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A new development in the hierarchical clustering of repertory grid data

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

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A new development in the hierarchical clustering of repertory grid data

  1. 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. 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. 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. 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. 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. 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. 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. 8. SaSarah‘s  grid  
  9. 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. 10. Standard  hierarchical  cluster  analysis  
  11. 11. Sar r Sarah‘s  grid  
  12. 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. 13. Descriptive Inference r = 0.35 r ∈ [0.3;0.4]
  14. 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. 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. 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. 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. 18. What  about  dendrograms?   No  indica9on   of  associa9on  
  19. 19. Element  „Child  self“  omibed     Dendrograms   are  based  on   similari9es  and   will  be  affected   by  element   selec9on  
  20. 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. 21. ①   ②   ③   Dendrogram   ①  AB|CDEF   ②  ABCD|EF   ③  ABC|DEF   Corresponding   Par33ons   A   B   C   D   E   F  
  22. 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. 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. 24. Bootstrap  Probabili9es    
  25. 25. Approximately  Unbiased  
  26. 26. AU  and  BP  
  27. 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. 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. 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. 30. Manhaban   Single  linkage  
  31. 31. Manhaban   Complete    linkage  
  32. 32. Euclidean   Single  linkage  
  33. 33. Euclidean   Complete  linkage  
  34. 34. 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  
  35. 35. www.onair.openrepgrid.org
  36. 36. Thanks !
  37. 37. 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  

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