A new development in the hierarchical clustering of repertory grid data
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The document discusses advancements in the hierarchical clustering of repertory grid data, particularly the concepts of tightness and looseness in construct systems. It details methods for measuring these constructs using the repertory grid and recent computational techniques for identifying significant clusters without traditional distributions. The authors highlight the implications for therapy and the need for further research to validate significant clusters in construct systems.
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A new development in the hierarchical clustering of repertory grid data
- 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)
- 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
- 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
- 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?
- 31. Manhaban 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
- 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