Description

A method for identifying structures in construct system is cluster analysis. Any distance or similarity measure accounting for a certain type of association could be used as a cluster criterion. Traditionally mostly Euclidean and Manhattan distances have been used. The earliest implementation of a cluster algorithm for repertory grids was incorporated in the program FOCUS (Shaw & Thomas, 1978).

Several distance measure can be selected (explanations from ?dist dcoumentation):

Also several cluster methods can be selected (explanations from ?hclust documentation).

The other methods can be regarded as aiming for clusters with characteristics somewhere between the single and complete link methods:

The distance and cluster methods can be combined as wished.

R-Code

Clustering

When the function cluster is called dendrograms of the construct and element clustering are drawn.

cluster(bell2010)

The function also returns the reordered matrix invisibly. To see the reordered grid save it into a new object. To oppress the creation of a graphic set print = FALSE.

x <- cluster(bell2010, print=FALSE)
x

RATINGS:
er (or the person who fill - 5 6 - A person of the opposite 
 A teacher you respected - 4 | | 7 - the unhappiest person y
friend of the same sex - 3 | | | | 8 - A person of the oppos
 you did not respect - 2 | | | | | | 9 - A person you work w
fident person you  - 1 | | | | | | | | 10 - self            
                     | | | | | | | | | |                    
  loves sports (1)   5 5 5 4 4 6 1 2 2 2   (1) dislikes spor
   transparent (2)   3 5 4 5 1 2 3 1 2 2   (2) not transpare
orried & tense (3)   6 2 4 5 2 3 2 3 6 4   (3) relaxed      
        gentle (4)   5 2 2 3 1 1 2 4 3 3   (4) rough        
     sensitive (5)   5 6 2 4 2 3 3 4 4 4   (5) insensitive  
(academically) (6)   1 1 1 1 4 2 2 3 4 2   (6) not so smart 
  loves people (7)   1 4 1 2 3 2 3 2 1 2   (7) not interacti
      fearless (8)   2 3 4 3 5 3 4 2 3 3   (8) fearful&timid
loves to argue (9)   1 3 3 4 4 2 2 1 3 3   (9) accept as it 

The function also allows to only cluster constructs or elements. To only cluster the constructs us the following code. Again a dendrogram is drawn and a grid with reordered constructs is returned.

x <- cluster(bell2010, along=1, print=FALSE)
x

RATINGS:
er (or the person who fill - 5 6 - A person of the opposite 
 A teacher you respected - 4 | | 7 - the unhappiest person y
friend of the same sex - 3 | | | | 8 - A person you work wel
 you did not respect - 2 | | | | | | 9 - self               
fident person you  - 1 | | | | | | | | 10 - A person of the 
                     | | | | | | | | | |                    
  loves sports (1)   5 5 5 4 4 6 1 2 2 2   (1) dislikes spor
   transparent (2)   3 5 4 5 1 2 3 2 2 1   (2) not transpare
orried & tense (3)   6 2 4 5 2 3 2 6 4 3   (3) relaxed      
        gentle (4)   5 2 2 3 1 1 2 3 3 4   (4) rough        
     sensitive (5)   5 6 2 4 2 3 3 4 4 4   (5) insensitive  
(academically) (6)   1 1 1 1 4 2 2 4 2 3   (6) not so smart 
  loves people (7)   1 4 1 2 3 2 3 1 2 2   (7) not interacti
      fearless (8)   2 3 4 3 5 3 4 3 3 2   (8) fearful&timid
loves to argue (9)   1 3 3 4 4 2 2 3 3 1   (9) accept as it 

To only cluster the elements set along=2.

x <- cluster(bell2010, along=2, print=FALSE)
x

RATINGS:
er (or the person who fill - 5 6 - A person of the opposite 
 A teacher you respected - 4 | | 7 - the unhappiest person y
friend of the same sex - 3 | | | | 8 - A person of the oppos
 you did not respect - 2 | | | | | | 9 - A person you work w
fident person you  - 1 | | | | | | | | 10 - self            
                     | | | | | | | | | |                    
   transparent (1)   3 5 4 5 1 2 3 1 2 2   (1) not transpare
  loves sports (2)   5 5 5 4 4 6 1 2 2 2   (2) dislikes spor
        gentle (3)   5 2 2 3 1 1 2 4 3 3   (3) rough        
orried & tense (4)   6 2 4 5 2 3 2 3 6 4   (4) relaxed      
     sensitive (5)   5 6 2 4 2 3 3 4 4 4   (5) insensitive  
  loves people (6)   1 4 1 2 3 2 3 2 1 2   (6) not interacti
(academically) (7)   1 1 1 1 4 2 2 3 4 2   (7) not so smart 
loves to argue (8)   1 3 3 4 4 2 2 1 3 3   (8) accept as it 
      fearless (9)   2 3 4 3 5 3 4 2 3 3   (9) fearful&timid

To apply different distance measures and cluster methods us the arguments dmethod and cmethod (here manhattan distance and single linkage clustering).

x <- cluster(bell2010, dmethod="manh", cmethod="single", print=FALSE)
x

RATINGS:
rson of the opposite sex t - 5 6 - A person you work well wi
 (or the person who fill - 4 | | 7 - A teacher you respected
friend of the same sex - 3 | | | | 8 - the unhappiest person
onfident person you  - 2 | | | | | | 9 - A person of the opp
ou did not respect - 1 | | | | | | | | 10 - self            
                     | | | | | | | | | |                    
(academically) (1)   7 7 7 4 5 4 7 6 6 6   (1) smart (academ
ot interactive (2)   4 7 7 5 6 7 6 5 6 6   (2) loves people 
 fearful&timid (3)   5 6 4 3 6 5 5 4 5 5   (3) fearless     
ccept as it is (4)   5 7 5 4 7 5 4 6 6 5   (4) loves to argu
ot transparent (5)   3 5 4 7 7 6 3 5 6 6   (5) transparent  
     sensitive (6)   6 5 2 2 4 4 4 3 3 4   (6) insensitive  
        gentle (7)   2 5 2 1 4 3 3 2 1 3   (7) rough        
orried & tense (8)   2 6 4 2 3 6 5 2 3 4   (8) relaxed      
  loves people (9)   4 1 1 3 2 1 2 3 2 2   (9) not interacti

To apply different methods to the constructs and the rows, use a two-step approach.

# cluster constructs using default methods
x <- cluster(bell2010, along=1, print=FALSE)       
# cluster elements using manhattan distance and single linkage clustering
x <- cluster(x, along=2, dm="manh", cm="single", print=FALSE)  
x

RATINGS:
rson of the opposite sex t - 5 6 - the unhappiest person you
t friend of the same sex - 4 | | 7 - A teacher you respected
er you did not respect - 3 | | | | 8 - A person of the oppos
 the person who fill - 2 | | | | | | 9 - A person you work w
fident person you  - 1 | | | | | | | | 10 - self            
                     | | | | | | | | | |                    
   insensitive (1)   3 6 2 6 5 5 4 4 4 4   (1) sensitive    
         rough (2)   3 7 6 6 7 6 5 4 5 5   (2) gentle       
       relaxed (3)   2 6 6 4 5 6 3 5 2 4   (3) worried & ten
  loves people (4)   1 3 4 1 2 3 2 2 1 2   (4) not interacti
(academically) (5)   1 4 1 1 2 2 1 3 4 2   (5) not so smart 
loves to argue (6)   1 4 3 3 2 2 4 1 3 3   (6) accept as it 
      fearless (7)   2 5 3 4 3 4 3 2 3 3   (7) fearful&timid
   transparent (8)   3 1 5 4 2 3 5 1 2 2   (8) not transpare
  loves sports (9)   5 4 5 5 6 1 4 2 2 2   (9) dislikes spor

Some other options can be set. Paste the code into the R console to try it out. See ?cluster for more information.

cluster(bell2010, main="My cluster analysis")   # new title
cluster(bell2010, type="t")                     # different drawing style
cluster(bell2010, dmethod="manhattan")          # using manhattan metric
cluster(bell2010, cmethod="single")             # do single linkage clustering
cluster(bell2010, cex=1, lab.cex=1)             # change appearance
cluster(bell2010, lab.cex=.7,                   # advanced appearance changes
        edgePar = list(lty=1:2, col=2:1))

Bootsrapped clustering

TODO

Clustered Bertin

The following figure shows a clustered Bertin matrix. The full explanation is found under the section Bertin display.

bertinCluster(bell2010)

Literature

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