Chapter 19

 

Measuring Treatment

 

Merle Canfield

 

 

During the past 50 years there has been a steady increase in the number of schools or styles of psychotherapy. In 1984 Karasu, T., et. al. reported 418 systems.  At the same time there has been a moderate increase in the elements of psychotherapy.  In recent years there has been a trend to merge these systems with common factors.  It is the purpose of this section to show how research designs empirically support the process of sorting out the characteristics of these system.  At the same time the designs should support the further elaboration and search for the elements of psychotherapy.  Frank (1971) proposed that there were common factors in addition to specific factors in psychotherapy that might be related to outcome (see also Parloff, 1986). 

In an attempt to determine whether the treatment has been implemented three approaches have been used: (1) developing therapy manuals, (2) labeling or coding psychotherapy as it unfolds, and (3) rating the process by the use of scales.  In 1979 Russell and Stiles reviewed the coding systems and attempted to devise a taxonomy and resulting coding system that would include all elements of the existing coding systems.  They generated a logical or rational taxonomy.  Although their task was different they did attempt do develop a taxonomy of the psychotherapeutic elements.  Many of the taxonomies that have been developed have been developed for specific style of school of therapy.  We are proposing methods to perform empirical taxonomies, or a combination of judgments and empirical

These methods can be used in to ways: (1) develop a taxonomy of the styles of therapy, or (2) develop a taxonomy of the elements of therapy.  Probably both of these would be useful.  If both were developed they would complement each other so that identifying a particular style or school of therapy would be a matter of selecting a set of elements of therapy.  The techniques are similar for the two areas.  Finally, modes other than psychotherapy are presented.

For example, of the 400 different schools what is the overlap and how would one determine the overlap between the schools?  It would be useful to identify the overlap or common factors.

What are the interactions that would place a therapeutic interaction within a specific school and separate the interaction from other schools (unique factors)?  What therapeutic interactions overlap with other schools (common factors).  There are two major tasks to be accomplished if one is to make such discriminations.  The first task is to be able to identify and measure (either by counting or by assessing some degree) of the client/therapist interactions.  If that can be accomplished the second task is to indicate the taxonomy of performances that each of the styles need.  That is, a profile of the style in terms of the performances is needed. The most fruitful method of identifying these performances has been to code the utterances of the psychotherapy process. 

There are four statistical methods that might be used for this process: (1) cluster analysis, (2) discriminant function analysis, (3) multidimensional scaling, and (4) factor analysis.  Four basic therapy processes discussed are: (1) psychotherapy, (2) group therapy, (3) ancillary therapies, and (3) milieu therapy.  The literature indicates that the descriptive or taxonomy process has be accomplished most the psychotherapy, next with group therapy, next the ancillary therapies and finally milieu is the least identified.

Trochim (19--) and _______________ used a combination of cluster analysis and multidimensional scaling to develop maps of attitudes of toward organizations.  It is proposed here that the same method could be used to build a taxonomy of the elements of psychotherapy. 


In this example participants were asked to identify processes or characteristics of psychotherapy that they thought were curative.  The following is that list (along with an abbreviated name):

Develop insight                                               INSIGHT

desensitize                                           DESENS

reflect                                                  REFLECT

introspection                                       INTROSP

develop trust                                       DEVTRUST

reframe                                                REFRAME

acceptance                                           ACCEPT

interpret                                               INTERP

being consistent                                  CONSIT

being nurturing                                               BEINGNUR

address anxiety                                                ADDRESA

correct faulty cognition                                   CORRECT

try new behaviors                                TRYBEHAV

challenge                                             CHALLENG

set limits                                              SETLIMIT

help cope                                            HLPCOPE

define expectations                             DEFEXP

demythetize                                         DEMYTH

counter transference                            CONTRAN

be a good mom                                              BGDMOM

identify conflicts                                  IDCONFL

These statements were put on slips of paper and the participants were asked to place them into stacks.  They were instructed that there must be fewer stacks than slips of paper and there must be more than one stack.  Once these stacks were created the information was transferred to a coding sheet in the following manner (the coding sheet is on the following page).  Assume that ACCEPT, DEVTRUST, BEINGNUR, and BGDMOM were placed in the same stack.  Marks would be place on the coding sheet at the intersection of all of these pairs.  Note that there is a mark where DEVTRUST intersects with DEVTRUST, ACCEPT, BEINGNUR, AND BGDMOM.  Again there is a mark where ACCEPT intersects with DEVTRUST, ACCEPT, BEINGNUR, and BGDMOM.  The same procedure is performed for BEINGNUR and BGDMOM.  The coding sheet has the marks filled in for this one stack (DEVTRUST, ACCEPT, BEINGNUR and BGDMOM).  The same sheet would be used to complete the remaining stacks.

Twenty-four participants completed the task of sorting the items and completing the tally sheets.  The cells of a summary sheet were then completed by counting the number of participants who had a check (or one (1)) in each in the corresponding cell.  That data is presented in Frame CURET.DBF the labels across the top are not part of the file.  The tallies are the number students who raised their hand when the cells were identified.  The tallies are actually an estimate of the number of hands raised when they were more than about 5.  The cells now give an indication of the similarity of the items or labels for the cell.  For example, the cell in Figure __ identified by REFRAME and REFLECT is 12 indicating that 12 of the respondents put those two items in the same stack.  That indicates a moderate to high similarity of the items.  The cell labeled CHALLENG and DEVTRUST has a 0 indicating that none of the respondents put those two items in the same stack and therefore judge them to be dissimilar.  Consequently, a high score indicates similarity and a low score indicates dissimilarity.  The upper right triangle and lower left of the triangle are identical.  The estimates were in fact not identical (because of errors in estimation) but the computer program requires and the lower left was used to duplicate the upper right.

        Figure 1.  A coding sheet for recording .....

 

 

 

NAME

 

INSIGHT

 

DESENS

 

REFLECT

 

INTROSP

 

DEVTRUST

 

REFRAM

 

ACCEPT

 

INTERP

 

CONSIT

 

BEINGNUR

 

ADDRESA

 

CORRECT

 

TRYBEHAV

 

CHALLENG

 

SETL

IMI

T

 

HLPCOPE

 

DEFEXP

 

DEMYTH

 

CONTRAN

 

BGDMOM

 

IDCONFL

 

INSIGHT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DESENS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

REFLECT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

INTROSP

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DEVTRUST

 

 

 

 

 

 

 

 

 

1

 

 

 

1

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

REFRAM

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ACCEPT

 

 

 

 

 

 

 

 

 

1

 

 

 

1

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

INTERP

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CONSIT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

BEINGNUR

 

 

 

 

 

 

 

 

 

1

 

 

 

1

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

ADDRESA

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CORRECT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TRYBEHAV

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHALLENG

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SETLIMIT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

HLPCOPE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DEFEXP

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DEMYTH

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CONTRAN

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

BGDMOM

 

 

 

 

 

 

 

 

 

1

 

 

 

1

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

IDCONFL

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2.  Representation of data base file CURET.DBF  (in dBase IV format).

 

 

 

NAME

 

INSIGHT

 

DESENS

 

REFLECT

 

INTROSP

 

DEVTRUST

 

REFRAM

 

ACCEPT

 

INTERP

 

CONSIT

 

BEINGNUR

 

ADDRESA

 

CORRECT

 

TRYBEHAV

 

CHALLENG

 

SETL

IMI

T

 

HLPCOPE

 

DEFEXP

 

DEMYTH

 

CONTRAN

 

BGDMOM

 

IDCONFL

 

INSIGHT

 

24

 

6

 

6

 

10

 

2

 

6

 

1

 

8

 

0

 

1

 

5

 

1

 

4

 

2

 

3

 

7

 

2

 

6

 

5

 

1

 

7

 

DESENS

 

6

 

24

 

4

 

4

 

0

 

5

 

0

 

2

 

1

 

0

 

12

 

5

 

6

 

6

 

4

 

6

 

3

 

6

 

4

 

1

 

5

 

REFLECT

 

6

 

4

 

24

 

6

 

3

 

12

 

5

 

8

 

4

 

4

 

4

 

3

 

2

 

4

 

2

 

3

 

3

 

8

 

3

 

2

 

6

 

INTROSP

 

10

 

4

 

6

 

24

 

3

 

5

 

3

 

12

 

1

 

2

 

4

 

2

 

4

 

3

 

2

 

2

 

0

 

7

 

5

 

2

 

4

 

DEVTRUST

 

2

 

0

 

3

 

3

 

24

 

2

 

18

 

1

 

12

 

14

 

1

 

2

 

1

 

0

 

4

 

3

 

3

 

3

 

1

 

12

 

2

 

REFRAM

 

6

 

5

 

12

 

5

 

2

 

24

 

3

 

4

 

5

 

2

 

5

 

5

 

5

 

7

 

2

 

5

 

3

 

9

 

2

 

2

 

4

 

ACCEPT

 

1

 

0

 

5

 

3

 

18

 

3

 

24

 

1

 

12

 

15

 

0

 

3

 

1

 

1

 

4

 

1

 

3

 

1

 

0

 

13

 

0

 

INTERP

 

8

 

2

 

8

 

12

 

1

 

4

 

1

 

24

 

1

 

0

 

2

 

5

 

2

 

4

 

3

 

2

 

2

 

7

 

7

 

1

 

3

 

CONSIT

 

0

 

1

 

4

 

1

 

12

 

5

 

12

 

1

 

24

 

9

 

1

 

4

 

1

 

0

 

7

 

2

 

6

 

0

 

0

 

9

 

0

 

BEINGNUR

 

1

 

0

 

4

 

2

 

14

 

2

 

15

 

0

 

9

 

24

 

0

 

3

 

1

 

1

 

3

 

1

 

3

 

1

 

0

 

15

 

0

 

ADDRESA

 

5

 

12

 

4

 

4

 

1

 

5

 

0

 

2

 

1

 

0

 

24

 

6

 

7

 

5

 

5

 

5

 

3

 

6

 

5

 

0

 

7

 

CORRECT

 

1

 

5

 

3

 

2

 

2

 

5

 

3

 

5

 

4

 

3

 

6

 

24

 

4

 

6

 

4

 

7

 

4

 

6

 

6

 

4

 

2

 

TRYBEHAV

 

4

 

6

 

2

 

4

 

1

 

5

 

1

 

2

 

1

 

1

 

7

 

4

 

24

 

9

 

6

 

7

 

3

 

4

 

2

 

1

 

4

 

CHALLENG

 

2

 

6

 

4

 

3

 

0

 

7

 

1

 

4

 

0

 

1

 

5

 

6

 

9

 

24

 

3

 

8

 

4

 

8

 

7

 

0

 

4

 

SETLIMIT

 

3

 

4

 

2

 

2

 

4

 

2

 

4

 

3

 

7

 

3

 

5

 

4

 

6

 

3

 

24

 

2

 

8

 

5

 

1

 

3

 

4

 

HLPCOPE

 

7

 

6

 

3

 

2

 

3

 

5

 

1

 

2

 

2

 

1

 

5

 

7

 

7

 

8

 

2

 

24

 

3

 

4

 

2

 

2

 

7

 

DEFEXP

 

2

 

3

 

3

 

0

 

3

 

3

 

3

 

2

 

6

 

3

 

3

 

4

 

3

 

4

 

8

 

3

 

24

 

8

 

1

 

3

 

6

 

DEMYTH

 

6

 

6

 

8

 

7

 

3

 

9

 

1

 

7

 

0

 

1

 

6

 

6

 

4

 

8

 

5

 

4

 

8

 

24

 

4

 

1

 

9

 

CONTRAN

 

5

 

4

 

3

 

5

 

1

 

2

 

0

 

7

 

0

 

0

 

5

 

6

 

2

 

7

 

1

 

2

 

1

 

4

 

24

 

0

 

6

 

BGDMOM

 

1

 

1

 

2

 

2

 

12

 

2

 

13

 

1

 

9

 

15

 

0

 

4

 

1

 

0

 

3

 

2

 

3

 

1

 

0

 

24

 

1

 

IDCONFL

 

7

 

5

 

6

 

4

 

2

 

4

 

0

 

3

 

0

 

0

 

7

 

2

 

4

 

4

 

4

 

7

 

6

 

9

 

6

 

1

 

24

 

 

The first method used to develop a taxonomy is cluster analysis.  It should be remembered that this process is a descriptive process and not hypothesis testing.  The purpose is to describe the relative position of one element to another.  The result of cluster analysis is a distance indicator of one element to another.  Frame CURCLS1.SPS is a jobstream for SPSS, Frame CURET.DBF contains the data in the dBase IV file that the jobstream will use.

 

 

File Name = curcls1.sps

 

get file =  '\proeval\curet.sav'/keep=

NAME      INSIGHT   DESENS    REFLECT   INTROSP   DEVTRUST  REFRAM   

ACCEPT    INTERP    CONSIT    BEINGNUR  ADDRESA   CORRECT   TRYBEHAV 

CHALLENG  SETLIMIT  HLPCOPE   DEFEXP    DEMYTH    CONTRAN   BGDMOM   

IDCONFL   .

cluster insight to idconfl

  /id=name

  /print=distance

  /print=schedule cluster(9)

  /plot=dendrogram hicicle.

 

 

 

 

 

 

┌───────────────────────────────────────────────────────────────────────────┐

│                               CURCLS1.LIS                                 │

├───────────────────────────────────────────────────────────────────────────┤

│Dendrogram using Average Linkage (Between Groups)                          │

│                                                                           │

│                          Rescaled Distance Cluster Combine                │

│                                                                           │

│    C A S E       0         5        10        15        20        25      │

│ Label       Seq  +‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+      │

│                                                                           │

│ DEVTRUST      5   ‑+‑‑‑+                                                  │

│ ACCEPT        7   ‑+   +‑‑‑‑‑+                                            │

│ BEINGNUR     10   ‑‑‑+‑+     +‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑+      │

│ BGDMOM       20   ‑‑‑+       |                                     |      │

│ CONSIT        9   ‑‑‑‑‑‑‑‑‑‑‑+                                     |      │

│ SETLIMIT     15   ‑‑‑‑‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑+                   |      │

│ DEFEXP       17   ‑‑‑‑‑‑‑‑‑‑‑‑‑+               |                   |      │

│ DESENS        2   ‑‑‑‑‑+‑‑‑‑‑‑‑‑‑‑‑‑‑+         |                   |      │

│ ADDRESA      11   ‑‑‑‑‑+             +‑+       |                   |      │

│ TRYBEHAV     13   ‑‑‑‑‑‑‑‑‑‑‑‑‑+‑+   | |       +‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑+      │

│ CHALLENG     14   ‑‑‑‑‑‑‑‑‑‑‑‑‑+ +‑‑‑+ +‑‑‑+   |                          │

│ HLPCOPE      16   ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑+     |   |   |                          │

│ CORRECT      12   ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑+   |   |                          │

│ REFLECT       3   ‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑‑‑+     +‑‑‑+                          │

│ REFRAME       6   ‑‑‑‑‑‑‑+           +‑‑‑+ |                              │

│ DEMYTH       18   ‑‑‑‑‑‑‑‑‑‑‑‑‑+‑‑‑‑‑+   | |                              │

│ IDCONFL      21   ‑‑‑‑‑‑‑‑‑‑‑‑‑+         +‑+                              │

│ INTROSP       4   ‑‑‑‑‑‑‑+‑‑‑‑‑+         |                                │

│ INTERP        8   ‑‑‑‑‑‑‑+     +‑‑‑‑‑‑‑+ |                                │

│ INSIGHT       1   ‑‑‑‑‑‑‑‑‑‑‑‑‑+       +‑+                                │

│ CONTRAN      19   ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑+                                  │

└───────────────────────────────────────────────────────────────────────────┘

The frame CURCLS1.LIS contains part of the output from the CURCLS1.SPS computer run.  The horizontal axis of the dendrogram represents distance  between the variables listed on the vertical axis.  Moving to the right indicates greater distance.  A plus (+) indicates that two variables have joined to form a cluster.  In the diagram DEVTRUST and ACCEPT were the first to join (when moving from left to right) are the most similar.  The next pair to join are BEINGNUR and BGDMOM indicating they are next pair in close proximity.  The next pair to join are DEFEXP and DESENS.  The next joining is not a pair of variables but the joining of two clusters; the cluster formed by DEVTRUST and ACCEPT is joined with BEINGNUR and BGDMOM.  The final joining (the further to the right) represents the joining of two clusters that are the most distant.  One of the clusters is made up of DEVTRUST, ACCEPT, BEINGUUR, and BGDMOM and the cluster to join it is made up of all of the other variables.  The method proposed for determining the number of clusters is to find the greatest horizontal distance where no variables or clusters join and draw a vertical line.  All clusters that have formed up to that line are considered to be clusters.  In the Figure that would be line A.  That is, there are no joinings between about 15 and 25; there is no other distance that great when no variables or clusters join.  Using that criteria there are two clusters in this solution since there are two clusters to the left of line A.  This solution is not very satisfying theoretically.  Many of the elements in cluster two seem different it does not help our taxonomy to combine them all in a single cluster.  Like factor analysis there is a second method for determining the number of clusters and that is interpretability.  Further, we are not testing hypotheses but building a taxonomy.  The next greatest distance when no joinings occur is at line B.  That vertical line intersects 9 horizontal lines indicating that 9 clusters have be formed up to that point.  The 9 clusters are presented along with the cluster names.

 

1.  Intrapshychic

INSIGHT 

INTROSP  

INTERP   

 

2.  Anxiety

DESENS  

ADDRESA  

 

3.  Give Feedback

REFLECT 

REFRAME   


4.  Warmth

DEVTRUST

ACCEPT   

CONSIT   

BEINGNUR 

BGDMOM   

 

5.  Correct

CORRECT 

 

6.  Directive

TRYBEHAV

CHALLENG 

HLPCOPE  


7.  Set Limits

SETLIMIT

DEFEXP   

 

8.  ??

DEMYTH  

IDCONFL  

 

9.  Countertransference

CONTRAN 


 

 

This solution appears to give a better taxonomy than does the first solution.  Cluster 1 INSIGHT, INTROSP, and INTERP would appear to similar type of therapist interventions; REFLECT and REFRAME are similar and so forth.  There are two clusters that contain single items and they do not seem to belong to any of the clusters that exists. 

Although there is some indication in the dendrogram of the distance between clusters it does not give a graphic picture.  For example, in the 9 cluster solution the distance between cluster REFLECT and REFRAME and the cluster SETLIMIT and DEFEXP is not readily apparent.  Is that distance about the same or much greater than the distance between DESENS and ADDRESA and the cluster SETLIMIT and DEFEXP?

The method of multidimensional scaling offers a more graphic picture of the distance between variables.  The following jobstream uses the same set of data as that used in the cluster analysis.  The task requests a three dimension solution.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

File Name = curcls3.sps

 

get file = '\proeval\curet.sav'/keep=

NAME      INSIGHT   DESENS    REFLECT   INTROSP   DEVTRUST  REFRAM   

ACCEPT    INTERP    CONSIT    BEINGNUR  ADDRESA   CORRECT   TRYBEHAV 

CHALLENG  SETLIMIT  HLPCOPE   DEFEXP    DEMYTH    CONTRAN   BGDMOM   

IDCONFL   .

als var = insight to idconfl

 /level=ordinal(similar)

 /criteria=dimensions(3)

 /plot=all.

 

 

The weights for each item on the three dimensions are presented in Frame CURALS3.LST.

 

 

┌─────────────────────────────────────────────────────────────────────────┐

│                            CURALS3.LST                                  │

├─────────────────────────────────────────────────────────────────────────┤

│  Dimension 1               Dimension 2                Dimension 3       │

├─────────────────────────────────────────────────────────────────────────┤

│BEINGNUR   ‑2.2475        INTROSP    ‑1.5347         CORRECT    ‑1.2737  │

│ACCEPT     ‑2.1976        INTERP     ‑1.4272         CONTRAN    ‑1.1266  │

│BGDMOM     ‑2.1645        REFLECT    ‑1.1540         CHALLENG   ‑0.9879  │

│CONSIT     ‑2.1478        CONTRAN    ‑1.0630         REFRAME    ‑0.8759  │

│DEVTRUST   ‑1.8399        INSIGHT    ‑0.9176         HLPCOPE    ‑0.6125  │

│DEFEXP     ‑0.4503        ACCEPT     ‑0.4117         TRYBEHAV   ‑0.4709  │

│SETLIMIT   ‑0.4328        DEVTRUST   ‑0.3511         BGDMOM     ‑0.2777  │

│CORRECT    ‑0.1885        BEINGNUR   ‑0.3222         INTROSP    ‑0.2690  │

│REFLECT    ‑0.0692        DEMYTH     ‑0.2027         DESENS     ‑0.1460  │

│REFRAME     0.0569        REFRAME    ‑0.1758         BEINGNUR   ‑0.0709  │

│INTROSP     0.3780        BGDMOM     ‑0.0736         ADDRESA    ‑0.0234  │

│HLPCOPE     0.5617        IDCONFL     0.0142         INTERP     ‑0.0207  │

│TRYBEHAV    1.0587        CONSIT      0.4554         ACCEPT      0.0023  │

│DEMYTH      1.0670        CORRECT     0.5163         CONSIT      0.0217  │

│INTERP      1.0758        CHALLENG    0.6593         REFLECT     0.3745  │

│IDCONFL     1.1449        ADDRESA     0.7462         DEVTRUST    0.6676  │

│INSIGHT     1.1548        DESENS      0.8300         DEMYTH      0.7658  │

│CHALLENG    1.1846        SETLIMIT    0.9680         INSIGHT     0.8362  │

│CONTRAN     1.2479        DEFEXP      1.0765         SETLIMIT    1.1014  │

│ADDRESA     1.3813        HLPCOPE     1.1151         IDCONFL     1.1337  │

│DESENS      1.4265        TRYBEHAV    1.252?         DEFEXP      1.2520  │

└─────────────────────────────────────────────────────────────────────────┘

It should be noted that this is not direct output from the SPSS run CURALS3.SPS, each dimension has been arranged from the most negative weight to the most positive weight.  Dimension 1 has at one pole BEINGNUR, ACCEPT, BGDMOM, CONSIT, and DEVTRUST while the other pole is DESENS, ADDRESA, CONTRAN, CHALLENG, and INSIGHT.  This dimension seems to be warmth (possibly emotional) to relearning (possibly cognitive).  Dimension 2 has at one pole INTROSP, INTERP, REFLECT, CONTRAN, and INSIGHT; at the other pole is TRYBEHAV, HLPCOPE, DEFEXP, and SETLIMIT.  The continuum seems to go from intrapsychic understanding to a directive or didactic approach.  The third dimension has CORRECT, CONTRAN, CHALLENG, and REFRAME at one pole and DEFEXP, IDCONFL, and SETLIMIT at the other pole.  Dimensions 1 and 2 have been plotted in the next figure while dimensions 1 and 3 have been plotted in the subsequent figure.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The figure gives a graphic picture of the distance between cluster 1 (from the previous calculation; DEVTRUST, ACCEPT, BEINGNUR, and BGDMOM) and cluster 2 (SETLIMIT and DEFEXP).  It also shows the distance between cluster 1 and cluster 3 (DESENS and ADDRESA; the variable CHALLENG is added to this cluster). Further, the distance between cluster 2 and cluster 3 is presented in this graphic.  It is important to remember that the task as presented here is not to test theory but develop taxonomies (in a sense to develop theory).  The task is to help the researcher visualize (understand) the complexities of the relationships among the variables.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Multidimensional scaling provides information beyond cluster analysis as presented here.  The two dimensions represented in the circumplex provides to additional bits of information: (1) distance between the clusters (and individual variables) and (2) where along each of dimensions each variable and cluster lies.  Although the dendrogram in cluster analysis does provide information of the distance between cluster 1 (INSIGHT, INTROSP, and INTERP) and cluster 3 (REFLECT and REFRAME) it is a much clearer in the circumplex model of multidimensional scaling.  Further, one can readily note the relation to other clusters.

Multidimensional scaling is not limited to two dimensions, like factor analysis there can be as many dimensions as their are variables and in the same manner that there can be as many factors as there are variables.  Unlike factor analysis the methods of determining the number of dimensions is not as advanced as is the method for determining the number of factors.  As multidimensional scaling is presented here that is not a problem

One could think of these 21 elements being used to describe a school or style of psychotherapy.  In a simplified form psychoanalysis might be thought of as made up of interpretation, transference and countertransference, and working through. 

 

This set of statistics can be used on a range of taxonomic or descriptive problems.  The creation of the input matrix determines the issue studied.  The method presented here combined the data from a panel as described by Trochim.  This process assists the clinician in sorting out their judgments.  However, a single clinician could fill in the above chart by making judgments of the similarity of the pairs (zero might represent similar--or no difference while 8 might represent a great difference).  In the cell identified by ACCEPT (acceptance) and BEINGNUR (being nurturing) the judgment might be 1 (quite similar).  The cell identified by DEVTRUST and CHALLENG might be judged 6 (quite dissimilar).  The same set of statistics could then be computed on the matrix of this single clinician.  This would result in a map of the clinician.  Such maps could be used be used in comparing theories.  Students could be compared to a panel of experts.  These methods could be used to empirically support the judgements of clinicians.

 

                                                                Personality Theory Rating Scale

 

Name: _________________________________________   Date: ________________

 

Use the scale below to rate the personality theory of ____________________________.

 

╔═══════════════════════════════════════════════════════════════════════════╗

║ None           A Little          Somewhat        Quite a Bit        A Lot ║

╟───────────────────────────────────────────────────────────────────────────╢

║ 0        1        2        3        4        5        6        7        8 ║

╚═══════════════════════════════════════════════════════════════════════════╝

                                                                            

                                  ╔══════════════════════╗                  

                                  ║LEAVE THE QUESTION    ║                  

                                  ║BLANK IF YOU DON'T    ║

                                  ║KNOW OR IF IT DOESN'T ║

                                  ║APPLY.                ║

                                  ╚══════════════════════╝

ACCORDING TO THIS THEORY:

 

   _____   ...motivation is based on drive reduction.

   _____   ...the person is an intentional (goal-oriented) being.

   _____   ...people are hedonistic.

   _____   ...cognition accounts for the actions of people.

   _____   ...values account for the actions of people.

   _____   ...people are actively involved in the development of their personality.

   _____   ...people's early experiences influence their personality.

   _____   ...the person imposes perception on the world.

   _____   ...the environment or learning accounts for the person's actions.

   _____   ...people are basically good.

   _____   ...heredity effects the person's actions.

   _____   This theory stresses the individual's conscious view of the world.

   _____   This theory stresses the individual's unconscious view of the world.

   _____   This theory stresses the individual's social consciousness.

   _____   This theory accounts for the individual's perception of reality.

   _____   This theory has influenced psychology (clinical, research, literature).

   _____   This theory focus on "the here and now", the past, or the future.

              (0 = past, 4 = here and now, 8 = future)

   _____   This theory is empirically based.

   _____   This theory is parsimonious.

   _____   This theory assumes that the individual has free choice.

   _____   This theory employs a method of therapeutic intervention.

   _____   This theory emphasizes psychopathology.

   _____   I agree with this theory.

The names for the respective items are as follows:

TDATE

THER

THID

CLUS

DRIVE

GOAL

HEDON

COG

VALUE

ACTIVE

EARLY

IMPOSE

LEARN

GOOD

HERED

CONSCI

UNCONS

SOCIAL

PERCEP

INFLU

TIME

DATA

PARSI

FREE

THERA

PATH

AGREE

 

    

The theorists rated were:

Freud              Sigmund Freud

ADLER           Alfred Adler

JUNG              Carl Jung

ROGERS         Carl Rogers

KELLY           George Kelly

HORNEY        Karen Horney

SULLIVI         Harry Stack Sullivan

BANDURA     Albert Bandura

CATTELL       Raymond B. Cattell

MASLOW      Abraham Maslow

BINSWAN      Ludwig Binswanger

ERIKSON       Erik Erikson

This data was part of a graduate student class assignment for students taking a theories of personality class.  Each week the students read the assignments and completed the questionnaire the day before the class meeting.  There were 17 students enrolled in the class, however, not all students complete the forms each week and consequently there is some missing data.  There were ___ completed forms.

In this first example the items of the questionnaire are grouped using factor analysis.  Recall that in this condition the items with similar profiles will be grouped together (into factors); not necessarily the items that are closest in distance (refer to the above discussion).  The data is in a dBase IV file with 9 indicating that data was omitted.  As can be seen mostly defaults were used in the computer run (see Frame PERFAC5.SPS) and a principle components extraction method was used and the rotation was orthoginal.  Using the eigenvalue of 1.00 is usually not considered the best method of deciding upon the number of factors; however, both interpretation and the scree method seemed also to indicate 5 factors.

 

File Name = perfac5.sps

 

get file= '\proeval\perall4.sav'/keep=

tDATE     THER      THID      CLUS      DRIVE    

GOAL      HEDON     COG       VALUE     ACTIVE    EARLY     IMPOSE    LEARN    

GOOD      HERED     CONSCI    UNCONS    SOCIAL    PERCEP    INFLU     TIME     

DATA      PARSI     FREE      THERA     PATH      AGREE .

missing values drive to agree (9).

fac var= drive to agree

   /missing=pairwise

   /plot=eigen

   /criteria=factors(5)

   /rotate.

 

 

 

 

┌────────────────────────────────────────────────────────────────────────────┐

│                                  PERFAC5.LIS                               │

├────────────────────────────────────────────────────────────────────────────┤

│Final Statistics:                                                           │

│                                                                            │

│Variable     Communality  *  Factor   Eigenvalue   Pct of Var   Cum Pct     │

│                          *                                                 │

│DRIVE             .54238  *     1       6.98937       30.4         30.4     │

│GOAL              .50485  *     2       2.15730        9.4         39.8     │

│HEDON             .54444  *     3       1.72904        7.5         47.3     │

│COG               .56063  *     4       1.47348        6.4         53.7     │

│VALUE             .66169  *     5       1.32890        5.8         59.5     │

│ACTIVE            .70979  *                                                 │

│EARLY             .58670  *                                                 │

│IMPOSE            .64661  *                                                 │

│LEARN             .58716  *                                                 │

│GOOD              .51995  *                                                 │

│HERED             .58137  *                                                 │

│CONSCI            .64024  *                                                 │

│UNCONS            .68112  *                                                 │

│SOCIAL            .61566  *                                                 │

│PERCEP            .61891  *                                                 │

│INFLU             .59501  *                                                 │

│TIME              .58200  *                                                 │

│DATA              .56921  *                                                 │

│PARSI             .60125  *                                                 │

│FREE              .61128  *                                                 │

│THERA             .64608  *                                                 │

│PATH              .52881  *                                                 │

│AGREE             .54294  *                                                 │

│                                                                            │

│Rotated Factor Matrix:                                                      │

│                                                                            │

│          FACTOR  1     FACTOR  2     FACTOR  3     FACTOR  4     FACTOR  5 │

│                                                                            │

│DRIVE      ‑.67035**     ‑.10424       ‑.12588       ‑.21679        .13893  │

│GOAL        .44300        .44580*       .16215        .17344        .23128  │

│HEDON      ‑.72226**     ‑.01600        .14498        .01324        .03653  │

│COG         .50422*       .28914        .40228        .23887       ‑.06251  │

│VALUE       .15529        .79294**     ‑.08091       ‑.04701        .00768  │

│ACTIVE      .58000**      .41073        .21364        .39876       ‑.00630  │

│EARLY      ‑.69231**      .27344       ‑.13863        .07009        .09220  │

│IMPOSE      .22239        .23344       ‑.10607        .72878**      .01706  │

│LEARN       .02767        .45879        .49137*       .21355       ‑.29809  │

│GOOD        .57563**      .41920        .00750       ‑.00350        .11316  │

│HERED       .10169        .28821       ‑.34325       ‑.60077**     ‑.09606  │

│CONSCI      .55734**      .40202        .29750        .26467       ‑.09712  │

│UNCONS     ‑.48833*      ‑.19803       ‑.48205       ‑.38498        .15119  │

│SOCIAL     ‑.05895        .71266**      .26140        .18852        .02080  │

│PERCEP      .29944        .16227       ‑.10921        .69839**      .05684  │

│INFLU      ‑.10405        .01029        .21463       ‑.17453        .71242**│

│TIME        .72841**      .04942        .11085        .18045       ‑.06419  │

│DATA        .29151        .04499        .63344**     ‑.20723        .19498  │

│PARSI       .05321        .06473        .76207**      .00803        .11581  │

│FREE        .51295*       .32588        .28510        .39853        .04315  │

│THERA      ‑.13541       ‑.11914       ‑.26013        .24730        .69622**│

│PATH       ‑.51195*      ‑.08011       ‑.40072       ‑.11859        .29269  │

│AGREE      ‑.01068        .34696        .25436        .21198        .55930**│

└────────────────────────────────────────────────────────────────────────────┘

We were somewhat arbitrary in selecting 5 factors in this solution so that it would match with the five cluster solution in the cluster analysis solution that follows.  It should be noted that one should not be so casual in determining the number of factors in a solution; the reader is referred to chapter __ when testing for the number of factors.  In developing theory the researcher may do that in an armchair fashion, reviewing the literature or with exploratory factor analysis.  The major purpose here to compare factor analysis with cluster analysis so that the number of factors is done with that purpose in mind.

The factors in Figure __ are presented in two ways: (1) the criterion of .60 is used to determine whether a variable loads on a factor, (2) if a variable does not load on any factor then it is placed on the factor with the highest loading. 

 

Factor I

DRIVE            -.67

HEDON          -.72

EARLY           -.69

TIME              .73

---------

GOAL             .44

COG                .50

ACTIVE          .58

GOOD .58

CONSCI          .56

UNCONS        -.49

FREE              .51

PATH              -.51

Factor II

VALUE           .79

SOCIAL          .71

-----------

GOAL             .45

 

Factor III

DATA             .63

PARSI .76

----------

LEARN           .49

 

Factor IV

IMPOSE          .73

HERED           -.60

PERCEP          .70

 

Factor V

INFLU .71

THERA           .70

AGREE           .56

 

 

The next example shows how cluster analysis can be used to group the same set of data.  The data needs to be conditioned before the cluster analysis can be run.  The means are computed within each theorist for each item.  For example, the first item DRIVE for all respondents to Freud were summed and divided by the number of respondents (the number was also rounded to the nearest integer to keep it on the same scale).  The matrix was then transposed because the computer program requires that format for this problem.  This data is presented in the   frame THER11.sav.

 

 

ITEM

 

FREUD

 

ADLER

 

JUNG

 

ROGERS

 

KELLY

 

HORNEY

 

SULLIVA

 

BANDURA

 

CATTELL

 

MASLOW

 

BINSWAN

 

ERIKSON

 

DRIVE

 

8

 

2

 

3

 

2

 

2

 

3

 

4

 

1

 

3

 

4

 

2

 

4

 

GOAL

 

4

 

7

 

5

 

7

 

7

 

5

 

5

 

6

 

5

 

7

 

5

 

6

 

HEDON

 

7

 

3

 

2

 

2

 

2

 

4

 

4

 

2

 

3

 

4

 

3

 

3

 

COG

 

3

 

6

 

4

 

6

 

7

 

4

 

5

 

7

 

5

 

6

 

6

 

6

 

VALUE

 

4

 

6

 

5

 

6

 

4

 

4

 

5

 

5

 

4

 

6

 

6

 

6

 

ACTIVE

 

2

 

7

 

5

 

7

 

7

 

5

 

5

 

6

 

5

 

6

 

7

 

6

 

EARLY

 

8

 

7

 

4

 

5

 

4

 

6

 

6

 

5

 

4

 

5

 

4

 

7

 

IMPOSE

 

4

 

6

 

4

 

7

 

7

 

5

 

6

 

5

 

5

 

6

 

7

 

6

 

LEARN

 

3

 

6

 

3

 

5

 

5

 

6

 

6

 

7

 

6

 

5

 

5

 

6

 

GOOD

 

2

 

5

 

5

 

8

 

5

 

4

 

4

 

5

 

4

 

6

 

4

 

6

 

HERED

 

3

 

4

 

5

 

4

 

2

 

3

 

3

 

2

 

5

 

4

 

3

 

4

 

CONSCI

 

2

 

6

 

5

 

6

 

6

 

4

 

5

 

6

 

5

 

6

 

6

 

6

 

UNCONS

 

8

 

2

 

7

 

3

 

2

 

6

 

4

 

2

 

4

 

3

 

2

 

5

 

SOCIAL

 

4

 

7

 

3

 

6

 

5

 

5

 

6

 

6

 

5

 

5

 

5

 

6

 

PERCEP

 

5

 

6

 

5

 

7

 

7

 

5

 

6

 

6

 

5

 

6

 

7

 

5

 

INFLU

 

8

 

5

 

5

 

7

 

4

 

3

 

5

 

6

 

5

 

6

 

4

 

5

 

TIME

 

0

 

5

 

5

 

4

 

5

 

3

 

4

 

4

 

5

 

5

 

5

 

3

 

DATA

 

3

 

3

 

2

 

4

 

4

 

2

 

4

 

6

 

6

 

3

 

2

 

4

 

PARSI

 

4

 

5

 

3

 

5

 

6

 

4

 

4

 

5

 

5

 

5

 

3

 

5

 

FREE

 

2

 

5

 

3

 

7

 

7

 

5

 

4

 

6

 

4

 

6

 

7

 

5

 

THERA

 

7

 

5

 

6

 

7

 

6

 

5

 

6

 

5

 

3

 

3

 

5

 

5

 

PATH

 

7

 

3

 

5

 

3

 

3

 

6

 

5

 

3

 

4

 

3

 

4

 

4

 

AGREE

 

5

 

5

 

4

 

5

 

5

 

5

 

5

 

5

 

4

 

5

 

4

 

5

 

 

 

File Name = percls3.sps

 

get file = '\proeval\ther11.sav'/keep=

ITEM  FREUD     ADLER     JUNG      ROGERS    KELLY     HORNEY

SULLIVA    BANDURA   CATTELL   MASLOW    BINSWAN   ERIKSON.

cluster freud to erikson

  /id=item

  /print=distance

  /print=schedule cluster(5)

  /plot=dendrogram hicicle.

 

 

 

                                                                       


┌───────────────────────────────────────────────────────────────────────┐

│                                 PERCLS3.SPS                           │

├───────────────────────────────────────────────────────────────────────┤

│Dendrogram using Average Linkage (Between Groups)                      │

│                                                                       │

│                          Rescaled Distance Cluster Combine            │

│                                                                       │

│    C A S E       0         5        10        15        20        25  │

│ Label       Seq  +‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+  │

│                                                                       │

│ IMPOSE        8   ‑+‑+                                                │

│ PERCEP       15   ‑+ |                                                │

│ GOAL          2   ‑‑‑+‑+                                              │

│ COG           4   ‑+ | |                                              │

│ CONSCI       12   ‑+‑+ +‑‑‑+                                          │

│ ACTIVE        6   ‑+   |   +‑+                                        │

│ FREE         20   ‑‑‑‑‑+   | |                                        │

│ VALUE         5   ‑‑‑‑‑‑‑+‑+ +‑‑‑‑‑‑‑‑‑+                              │

│ GOOD         10   ‑‑‑‑‑‑‑+   |         |                              │

│ LEARN         9   ‑+‑‑‑‑‑+   |         |                              │

│ SOCIAL       14   ‑+     +‑‑‑+         +‑‑‑‑‑‑‑‑‑‑‑+                  │

│ PARSI        19   ‑+‑‑‑‑‑+             |           |                  │

│ AGREE        23   ‑+                   |           |                  │

│ INFLU        16   ‑‑‑‑‑‑‑‑‑‑‑‑‑+       |           +‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑+  │

│ THERA        21   ‑‑‑‑‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑+           |               |  │

│ EARLY         7   ‑‑‑‑‑‑‑‑‑‑‑‑‑+                   |               |  │

│ HERED        11   ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑+‑‑‑+             |               |  │

│ TIME         17   ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑+   +‑‑‑‑‑‑‑‑‑‑‑‑‑+               |  │

│ DATA         18   ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑+                             |  │

│ DRIVE         1   ‑+‑‑‑‑‑‑‑‑‑‑‑‑‑+                                 |  │

│ HEDON         3   ‑+             +‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑+  │

│ UNCONS       13   ‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+                                    │

│ PATH         22   ‑‑‑‑‑+                                              │

└───────────────────────────────────────────────────────────────────────┘

If five factors are chosen (to be comparable to the 5 factor solution above) there are as follows:

Cluster 1

IMPOSE

PERCEP

GOAL

COG

CONSCI

ACTIVE

 

FREE

VALUE

GOOD

LEARN

SOCIAL

PARSI

AGREE

Cluster 2

INFLU

THERA

EARLY

 

Cluster 3

HERED

TIME

DATA

Cluster 4

DATA

 

Cluster 5

DRIVE

HEDON

UNCONS

PATH

 

The first question is whether there is a difference between the factor analysis solution and the cluster analysis solution?  There is not a test of significance that can be run [or would Chi Square be appropriate? there is the problem of what is a match is it two or more variables in the same group; cluseter or factor or must all overlap] so it is mostly a matter determining whether it appears that the solutions are the same or different.  If one chooses to the criteria of two or more variables in the same group then it does not look too bad.  Four variables from cluster 1 can be found in factor 1; 3 variables from cluster 1 can be found in factor 2 (all of factor 2); 2 variables in cluster 2 can be found in factor 5; and 4 variables in cluster 5 can be found in factor 1.  That is 16 variables that overlap and 8 variables that do not [something wrong with this count].  That does give some indication that there is some fit of the two methods.  However, cluster 3 does not have any variables that are shared in any of the factors and factor 4 does not have any variables that are shared in any of the clusters.  Further, cluster 1 and factor 1 are fragmented across the two methods.  Finally, if one tries to develop a taxonomy from the two methods it would seem to be different for the two methods. 


 

File Name = perals4.sps

 

get file = '\proeval\therdtt.sav'/keep=

item

DRIVE     GOAL      HEDON     COG       VALUE     ACTIVE    EARLY    

IMPOSE    LEARN     GOOD      HERED     CONSCI    UNCONS    SOCIAL   

PERCEP    INFLU     TIME      DATA      PARSI     FREE      THERA    

PATH      AGREE.

ALS VAR=drive to agree

  /LEVEL=interval(disSIMILAR)

  /PLOT=ALL.

 

 

 

┌─────────────────────────────────────────────────────────────────────┐

│                  PERALS4.LST                                        │

├─────────────────────────────────────────────────────────────────────┤

│          Configuration derived in 2 dimensions                      │

│                  Stimulus Coordinates                               │

│                       Dimension                                     │

│Stimulus   Stimulus     1        2                                   │

│ Number      Name                                                    │

│                                                                     │

│   1      DRIVE      2.7576   ‑.0457                                 │

│   2      GOAL      ‑1.2316    .3747                                 │

│   3      HEDON      2.2009   ‑.2654                                 │

│   4      COG       ‑1.2308   ‑.1352                                 │

│   5      VALUE      ‑.2718    .1322                                 │

│   6      ACTIVE    ‑1.7376   ‑.0292                                 │

│   7      EARLY       .2737   1.2230                                 │

│   8      IMPOSE    ‑1.1493    .3867                                 │

│   9      LEARN      ‑.8091   ‑.2012                                 │

│  10      GOOD       ‑.7062   ‑.5612                                 │

│  11      HERED      1.1133   ‑.9480                                 │

│  12      CONSCI    ‑1.0615   ‑.3196                                 │

│  13      UNCONS     2.4200    .6935                                 │

│  14      SOCIAL     ‑.5909    .1727                                 │

│  15      PERCEP    ‑1.0926    .6262                                 │

│  16      INFLU       .2361    .9594                                 │

│  17      TIME       ‑.2709  ‑1.4354                                 │

│  18      DATA        .7070  ‑1.3658                                 │

│  19      PARSI       .1220   ‑.2902                                 │

│  20      FREE      ‑1.3629   ‑.4720                                 │

│  21      THERA       .0554   1.0593                                 │

│  22      PATH       1.4080    .3780                                 │

│  23      AGREE       .2212    .0633                                 │

└─────────────────────────────────────────────────────────────────────┘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The Euclidean Distance model in the above figure would seem to be helpful in developing a taxonomy of the variables under consideration.  Outlines have been drawn to show the variables that might go together in a group.  The problem with the dispersion is that there are no clear-cut distinctions between the variables; they seem to be on a continuum.  Consequently, the divisions are somewhat arbitrary.  It is a little like dividing age ranges into ten year categories.

In keeping with the models above of grouping the variables the following is the breakdown when five goups are specified.

Group 1

EARLY

THERA

INFLU

 

Group 2

PERCEP

IMPOSE

GOAL

SOCIAL

VALUE

AGREE

PARSI

Group 3

UNCONS

PATH

DRIVE

HEDON

 

Group 4

ACTIVE

COG

LEARN

CONSI

FREE

GOOD

Group 5

HERED

TIME

DATA

 

 

 

In the next example we use the same data set but focus on theorists rather than variables.  A taxonomy of theorists seems as useful as a taxonomy of variables [must be a better way to say that].  Cattell's cube could be useful in this context.  The data used in the cluster example is the same as the last cluster example but it was not transposed, it is in Frame THER1.TXT.

 

 

FNAME

 

DRIVE

 

GOAL

 

HEDON

 

COG

 

VALUE

 

ACTIVE

 

EARLY

 

IMPOSE

 

LEARN

 

GOOD

 

HERED

 

CONSCI

 

UNCONS

 

SOCIAL

 

PERCEP

 

INFLU

 

TIME

 

DATA

 

PARSI

 

FREE

 

THERA

 

PATH

 

AGREE

 

FREUD

 

8

 

4

 

7

 

3

 

4

 

2

 

8

 

4

 

3

 

2

 

3

 

2

 

8

 

4

 

5

 

8

 

0

 

3

 

4

 

2

 

7

 

7

 

5

 

ADLER

 

2

 

7

 

3

 

6

 

6

 

7

 

7

 

6

 

6

 

5

 

4

 

6

 

2

 

7

 

6

 

5

 

5

 

3

 

5

 

5

 

5

 

3

 

5

 

JUNG

 

3

 

5

 

2

 

4

 

5

 

5

 

4

 

4

 

3

 

5

 

5

 

5

 

7

 

3

 

5

 

5

 

5

 

2

 

3

 

3

 

6

 

5

 

4

 

ROGERS

 

2

 

7

 

2

 

6

 

6

 

7

 

5

 

7

 

5

 

8

 

4

 

6

 

3

 

6

 

7

 

7

 

4

 

4

 

5

 

7

 

7

 

3

 

5

 

KELLY

 

2

 

7

 

2

 

7

 

4

 

7

 

4

 

7

 

5

 

5

 

2

 

6

 

2

 

5

 

7

 

4

 

5

 

4

 

6

 

7

 

6

 

3

 

5

 

HORNEY

 

3

 

5

 

4

 

4

 

4

 

5

 

6

 

5

 

6

 

4

 

3

 

4

 

6

 

5

 

5

 

3

 

3

 

2

 

4

 

5

 

5

 

6

 

5

 

SULLIVA

 

4

 

5

 

4

 

5

 

5

 

5

 

6

 

6

 

6

 

4

 

3

 

5

 

4

 

6

 

6

 

5

 

4

 

4

 

4

 

4

 

6

 

5

 

5

 

BANDURA

 

1

 

6

 

2

 

7

 

5

 

6

 

5

 

5

 

7

 

5

 

2

 

6

 

2

 

6

 

6

 

6

 

4

 

6

 

5

 

6

 

5

 

3

 

5

 

CATTELL

 

3

 

5

 

3

 

5

 

4

 

5

 

4

 

5

 

6

 

4

 

5

 

5

 

4

 

5

 

5

 

5

 

5

 

6

 

5

 

4

 

3

 

4

 

4

 

MASLOW

 

4

 

7

 

4

 

6

 

6

 

6

 

5

 

6

 

5

 

6

 

4

 

6

 

3

 

5

 

6

 

6

 

5

 

3

 

5

 

6

 

3

 

3

 

5

 

BINSWAN

 

2

 

5

 

3

 

6

 

6

 

7

 

4

 

7

 

5

 

4

 

3

 

6

 

2

 

5

 

7

 

4

 

5

 

2

 

3

 

7

 

5

 

4

 

4

 

ERIKSON

 

4

 

6

 

3

 

6

 

6

 

6

 

7

 

6

 

6

 

6

 

4

 

6

 

5

 

6

 

5

 

5

 

3

 

4

 

5

 

5

 

5

 

4

 

5

 

 

 

File Name = percls2.sps

 

get file = '\proeval\ther1.sav'/keep=  

FNAME  DRIVE GOAL     HEDON    COG      VALUE    ACTIVE   EARLY

IMPOSE LEARN GOOD     HERED    CONSCI   UNCONS   SOCIAL   PERCEP  

INFLU  TIME  DATA     PARSI    FREE     THERA    PATH     AGREE.  

cluster drive to agree 

  /id=fname    

  /METHOD=WARD

  /print=distance      

  /print=schedule cluster(4)   

  /plot=dendrogram hicicle.

 

 

┌───────────────────────────────────────────────────────────────────────────┐

│                                PERCLS2.LIS                                │

├───────────────────────────────────────────────────────────────────────────┤

│Cluster Membership of Cases using Ward Method                              │

│                                                                           │

│                            Number of Clusters                             │

│                                                                           │

│ Label       Case      4                                                   │

│                                                                           │

│ Freud          1      1                                                   │

│ Adler          2      2                                                   │

│ Jung           3      3                                                   │

│ Rogers         4      2                                                   │

│ Kelly          5      2                                                   │

│ Horney         6      4                                                   │

│ Sulliva        7      4                                                   │

│ Bandura        8      2                                                   │

│ Cattell        9      4                                                   │

│ Maslow        10      2                                                   │

│ Binswan       11      2                                                   │

│ Erikson       12      4                                                   │

│                                                                           │

│Dendrogram using Ward Method                                               │

│                                                                           │

│                          Rescaled Distance Cluster Combine                │

│                                                                           │

│    C A S E       0         5        10        15        20        25      │

│ Label       Seq  +‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+      │

│                             ┌─┐         ┌─┐            ┌─┐                │

│                             │C│         │B│            │A│                │

│ Sulliva       7   ‑+‑‑‑+    └┬┘         └┬┘            └┬┘                │

│ Erikson      12   ‑+   +‑‑‑‑‑│‑+         │              │                 │

│ Horney        6   ‑‑‑‑‑+     │ +‑‑‑‑‑+   │              │                 │

│ Cattell       9   ‑‑‑‑‑‑‑‑‑‑‑│‑+     +‑‑‑│‑‑‑‑‑+        │                 │

│ Jung          3   ‑‑‑‑‑‑‑‑‑‑‑│‑‑‑‑‑‑‑+   │     |        │                 │

│ Adler         2   ‑+‑‑‑‑‑+   │           │     +‑‑‑‑‑‑‑‑│‑‑‑‑‑‑‑‑‑‑+      │

│ Maslow       10   ‑+     +‑‑‑│‑‑‑+       │     |        │          |      │

│ Binswan      11   ‑‑‑‑‑‑‑+   │   +‑‑‑‑‑‑‑│‑‑‑‑‑+        │          |      │

│ Kelly         5   ‑‑‑+‑‑‑‑‑+ │   |       │              │          |      │

│ Bandura       8   ‑‑‑+     +‑│‑‑‑+       │              │          |      │

│ Rogers        4   ‑‑‑‑‑‑‑‑‑+ │           │              │          |      │

│ Freud         1   ‑‑‑‑‑‑‑‑‑‑‑│‑‑‑‑‑‑‑‑‑‑‑│‑‑‑‑‑‑‑‑‑‑‑‑‑‑│‑‑‑‑‑‑‑‑‑‑+      │

└──────────────────────────────┴───────────┴──────────────┴─────────────────┘

 

Using the rules of  the vertical line should be drawn at line "A" giving 2 clusters.  They are not very interesting in that Freud is in a cluster alone and every other theorist is in the second cluster.  The next greatest horizontal distance is identified by line "B" which forms two clusters.  This might be the might be interpretable set but line "C" forming 6 clusters seems the most ______.  The clusters formed by this solution are as follows:

Cluster 1

Sullivan

Erikson

Horney

Cluster 2

Cattell

Cluster 3

Jung

Cluster 4

Adler

Maslow

Binswanger

Cluster 5

Kelly

Bandura

Rogers

Cluster 6

Freud

 

 

 

 

 

 

 

In this next set of data takes same data as and

 

 

File Name = perals6.sps

 

get file = '\proeval\therdis1.sav'

    /keep=

Freud   Adler    Jung    Rogers    Kelly    Horney

Sulliva Bandura  Cattell Maslow    Binswan  Erikson.

ALS VAR=Freud to Erikson

  /LEVEL=interval(disSIMILAR)

  /criteria=dimens(1)

  /METHOD=INDSCAL

  /PLOT=ALL.

 

 

 

┌──────────────────┐

│   PERALS6.LST    │

├──────────────────┤

│KELLY      ‑1.0647│

│ROGERS     ‑0.9488│

│BANDURA    ‑0.865 │

│BINSWAN    ‑0.75  │

│ADLER      ‑0.6355│

│MASLOW     ‑0.3176│

│CATTELL     0.0888│

│ERIKSON     0.145 │

│SULLIVA     0.3638│

│HORNEY      0.591 │

│JUNG        0.7265│

│FREUD       2.6668│

└──────────────────┘

              


 

 

 

 

File Name = perals3.sps

 

get file = '\proeval\therdis1.sav'

    /keep=

Freud   Adler    Jung    Rogers    Kelly    Horney

Sulliva Bandura  Cattell Maslow    Binswan  Erikson.

ALS VAR=Freud to Erikson

  /LEVEL=interval(disSIMILAR)

  /METHOD=INDSCAL

  /PLOT=ALL.

 

 

 

 

 

File Name = therdis1.sav

 

FREUD

 

ADLER

 

JUNG

 

ROGERS

 

KELLY

 

HORNEY

 

SULLIVA

 

BANDURA

 

CATTELL

 

MASLOW

 

BINSWAN

 

ERIKSON

 

0

 

249

 

145

 

276

 

295

 

121

 

126

 

270

 

189

 

218

 

263

 

167

 

249

 

0

 

96

 

33

 

34

 

66

 

33

 

29

 

52

 

23

 

34

 

24

 

145

 

96

 

0

 

103

 

110

 

46

 

55

 

115

 

58

 

77

 

82

 

66

 

276

 

33

 

103

 

0

 

33

 

101

 

60

 

38

 

81

 

36

 

49

 

39

 

295

 

34

 

110

 

33

 

0

 

84

 

55

 

27

 

64

 

39

 

28

 

54

 

121

 

66

 

46

 

101

 

84

 

0

 

23

 

83

 

50

 

65

 

62

 

38

 

126

 

33

 

55

 

60

 

55

 

23

 

0

 

44

 

31

 

38

 

43

 

19

 

270

 

29

 

115

 

38

 

27

 

83

 

44

 

0

 

43

 

42

 

47

 

41

 

189

 

52

 

58

 

81

 

64

 

50

 

31

 

43

 

0

 

39

 

62

 

40

 

218

 

23

 

77

 

36

 

39

 

65

 

38

 

42

 

39

 

0

 

35

 

25

 

263

 

34

 

82

 

49

 

28

 

62

 

43

 

47

 

62

 

35

 

0

 

54

 

167

 

24

 

66

 

39

 

54

 

38

 

19

 

41

 

40

 

25

 

54

 

0

 

 

┌──────────────────────────────────────────────────┐

│                   PERALS3.LST                    │

├──────────────────────────────────────────────────┤

│  Dimension 1                Dimension 2          │

│                                                  │

│KELLY        ‑1.4323      JUNG         ‑0.9577    │

│ROGERS       ‑1.2329      CATTELL      ‑0.7267    │

│BANDURA      ‑1.1546      BINSWAN      ‑0.653     │

│BINSWAN      ‑0.9693      KELLY        ‑0.2254    │

│ADLER        ‑0.8148      HORNEY       ‑0.0529    │

│MASLOW       ‑0.3965      FREUD         0.1277    │

│CATTELL       0.0739      SULLIVA       0.1736    │

│ERIKSON       0.2         BANDURA       0.3124    │

│SULLIVA       0.51        ERIKSON       0.4641    │

│JUNG          0.8239      ADLER         0.4963    │

│HORNEY        0.84        ROGERS        0.5       │

│FREUD         3.545       MASLOW        0.5358    │

└──────────────────────────────────────────────────┘

 

 

It produced the following chart:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cluster analysis and multidimensional are the similar when multidimensional scaling uses only one dimension.  This can be seen in comparing Dimension 1 and the Dendogram (not real sure of this one at this point--I'll check it further). 

The manner in which the data is entered for these programs makes a major difference in the results.  It is as important as choosing the proper statistics.  In the above example there were ______ manipulations of the data before it was entered into the program.  The participants completed a questionnaire about the theorists, each item was summed across the participants within each theorist, and the squared multiple distance between each theorist was computed.  It was the squared multiple distance that was used as input to the multidimensional scaling program.  In the following example the input to the program are direct judgments of a single judge.  The judge makes a decision about the distance between each pair of objects (in this instance personality theorists) based on personal attitudes, information, or __________.  

A single judge compared each theorist by using a scale from 0 to 8.  A zero (0) indicated that the theorists were identical and an 8 indicated that the theorists were most dissimilar.  The judge rated Freud and Adler as similar with a 3, and rated Jung as slightly more similar to Freud with a 2.  The rating of Bandura to Freud with an 8 indicates most dissimilarity.

 

 

 

 

File Name = therate.sav

 

THEORIST

 

FREUD

 

ADLER

 

JUNG

 

ROGERS

 

KELLY

 

HORNEY

 

SULLIVA

 

BANDURA

 

CATTELL

 

MASLOW

 

BINSWAN

 

ERIKSON

 

FREUD

 

0

 

3

 

2

 

5

 

6

 

4

 

4

 

8

 

8

 

5

 

6

 

5

 

ADLER

 

3

 

0

 

3

 

4

 

3

 

4

 

2

 

5

 

4

 

3

 

3

 

4

 

JUNG

 

2

 

3

 

0

 

4

 

3

 

4

 

3

 

7

 

7

 

2

 

2

 

4

 

ROGERS

 

5

 

4

 

4

 

0

 

3

 

5

 

3

 

5

 

6

 

2

 

3

 

5

 

KELLY

 

6

 

3

 

3

 

3

 

0

 

2

 

2

 

2

 

3

 

3

 

5

 

3

 

HORNEY

 

4

 

4

 

4

 

5

 

2

 

0

 

2

 

4

 

3

 

4

 

4

 

2

 

SULLIVA

 

4

 

2

 

3

 

3

 

2

 

2

 

0

 

3

 

2

 

3

 

4

 

1

 

BANDURA

 

8

 

5

 

7

 

5

 

2

 

4

 

3

 

0

 

2

 

4

 

4

 

3

 

CATTELL

 

8

 

4

 

7

 

6

 

3

 

3

 

2

 

2

 

0

 

3

 

3

 

2

 

MASLOW

 

5

 

3

 

2

 

2

 

3

 

4

 

3

 

4

 

3

 

0

 

1

 

4

 

BINSWAN

 

6

 

3

 

2

 

3

 

5

 

4

 

4

 

4

 

3

 

1

 

0

 

3

 

ERIKSON

 

5

 

4

 

4

 

5

 

3

 

2

 

1

 

3

 

2

 

4

 

3

 

0

 

The jobstream used to run the multidimensional scaling program in SPSS is as follows:

 

 

File Name = perals9.sps

 

get file = '\proeval\therate.sav'

    /keep=

THEORIST      FREUD     ADLER     JUNG      ROGERS   

KELLY     HORNEY    SULLIVA   BANDURA   CATTELL   MASLOW   

BINSWAN   ERIKSON.

ALS VAR=FREUD TO ERIKSON

  /LEVEL=INTERVAL(disSIMILAR)

  /PLOT=ALL.

 

 

It should be noted that the text file "THERATE.TXT" did not contain the names of the theorists on the first line.  The output of that computer run is in Frame PERALS9.LST.  One might ask the whether the two matrices are different.  For example, the group of judges might have been a panel of experts and the single rater might be a student and the question would be how close to the experts is the student?  On the other hand the categories might be diagnosis and the question might be different methods of establishing diagnoses: (1) structured interview, (2) psychological testing, or (3) clinical judgment.  There could seem to be a whole set of clinical judgment questions that these methods could be applied to.

We indicated in the above section that there is not a statistical method for determining  the grouping solutions of cluster analysis, factor analysis, or multidimensional scaling was different among themselves.  However, there are methods for determining whether the matrices themselves are significantly different.

 

┌────────────────────────────┐  

│     PERALS9.LST            │

├────────────────────────────┤

│             Dimension      │

│                            │

│Stimulus     1        2     │

│  Name                      │

│                            │

│Freud      2.1751    .8550  │

│ADLER       .8344    .3116  │

│JUNG       1.5860   ‑.1741  │

│ROGERS      .6082  ‑1.5110  │

│KELLY      ‑.6659    .3442  │

│HORNEY     ‑.2005   1.1608  │

│SULLIVA    ‑.1193    .4693  │

│BANDURA   ‑1.8848   ‑.1841  │

│CATTELL   ‑1.7805    .1339  │

│MASLOW      .1183   ‑.9897  │

│BINSWAN    ‑.0561  ‑1.2390  │

│ERIKSON    ‑.6148    .8230  │

└────────────────────────────┘

That data from Frame PERALS9.LST was used to create the following plot:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

If the categories are known then it might be desirable to predict the theorist.  Discriminant analysis allows one to determine which variables are most effective in predicting theorists and to develop a taxonomy for both the theorist and the variables.

 

 

File Name = perdsc2.sps

 

get file = '\proeval\perall4.sav'/keep=

THID      CLUS      DRIVE    

GOAL      HEDON     COG       VALUE     ACTIVE    EARLY     IMPOSE    LEARN    

GOOD      HERED     CONSCI    UNCONS    SOCIAL    PERCEP    INFLU     TIME     

DATA      PARSI     FREE      THERA     PATH      AGREE .

value labels thid

      1 'freud'    

      2 'Adler'    

      3 'Jung'     

      4 'Rogers'   

      5 'Kelly'    

      6 'Horney'   

      7 'Sulliva'  

      8 'Bandura'  

      9 'Cattell'  

     10 'Maslow'   

     11 'Binswan'  

     12 'Erikson'.

missing values drive to agree (9).

DSC GROUPS=thid(1,12)

 /VAR=drive to agree 

 /METHOD=MINRESID 

 /PIN=.05    

 /FUNCTIONS=6,100,.05

 /STATISTICS=MEAN STDDEV COEFF RAW TABLE.

 

 

 

                               Degrees of Freedom  Signif.   Between Groups

 Wilks' Lambda         .00238       18   11      172.0

 Approximate F        6.73348           198     1487.7   .0000

 RESIDUAL VARIANCE   12.98197

 

 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables in the analysis after step  18 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

 

 Variable  Tolerance  F to remove  Residual Variance

 DRIVE      .8086075    4.4085

 GOAL       .6885392    2.8517

 HEDON      .8205188    4.2216

 VALUE      .6899227    1.8635

 EARLY      .7400657    4.8709

 LEARN      .7701072    2.5441

 GOOD       .7114397    8.9138

 HERED      .8461894    3.0091

 CONSCI     .5652705    3.7762

 UNCONS     .5666565    4.9305

 SOCIAL     .6762921    2.1756

 PERCEP     .8453969    3.0534

 INFLU      .7347672    9.9031

 DATA       .7400053    7.9982

 FREE       .7024298    3.1230

 THERA      .6631685    4.7735

 PATH       .6396031    4.2841

 AGREE      .7558803    2.3188

 

 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables not in the analysis after step  18 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

 

                       Minimum   Signif. of

 Variable  Tolerance  Tolerance  F to enter   Residual variance

 COG        .7229042   .5566498     .6106

 ACTIVE     .5912503   .5277644     .2419

 IMPOSE     .6659893   .5559298     .6726

 TIME       .7545682   .5623679     .0731

 PARSI      .7565332   .5601723     .2784

 

 Canonical Discriminant Functions evaluated at Group Means (Group Centroids)

 

   Group      FUNC   1    FUNC   2    FUNC   3    FUNC   4    FUNC   5

        1       5.95297      .15154      .28629      .05561    ‑1.15760

        2       ‑.63536     ‑.27522     ‑.00035     1.83737     ‑.15173

        3       1.02702     1.23000      .55006    ‑1.87012      .81240

        4      ‑1.46471     1.63556     1.68544      .26381     ‑.08564

        5      ‑2.42486      .46351     ‑.56310     ‑.62008    ‑1.47778

        6        .87926     ‑.12746    ‑2.36745      .13268     1.08705

        7        .37195     ‑.86906     ‑.85952      .27647      .40472

        8      ‑1.46161    ‑1.49840      .54719      .30448     ‑.86419

        9       ‑.59271    ‑2.65032     1.03258    ‑1.18762      .46617

       10       ‑.35662      .98185      .87905      .46556      .93586

       11      ‑1.59251      .96399    ‑1.73615     ‑.52494     ‑.44835

       12        .31087     ‑.05714      .48770      .58778     1.10934

 

   Group      FUNC   6

        1       ‑.26492

        2        .35772

        3        .83661

        4        .56233

        5        .58221

        6        .63629

        7        .35528

        8        .01865

        9       ‑.44479

       10      ‑1.26531

       11      ‑1.41790

       12        .27400

 

 Pooled‑within‑groups correlations between discriminating variables

                                   and canonical discriminant functions

 (Variables ordered by size of correlation within function)

 

              FUNC  1    FUNC  2    FUNC  3    FUNC  4    FUNC  5    FUNC  6

 UNCONS        .48407*    .03096    ‑.09763    ‑.35571*    .26928     .43638*

 DRIVE         .45355*    .01335     .05730    ‑.03132     .06143    ‑.3268*

 CONSCI       ‑.44664*    .02689     .14508     .15771     .00853    ‑.08340

 ACTIVE       ‑.41748*    .02171     .18051     .18981    ‑.10032    ‑.03243

 FREE         ‑.37396*    .27632     .00144     .13380    ‑.16393    ‑.28372

 HEDON         .33958*   ‑.05369    ‑.10844     .32823*    .00075    ‑.17824

 PATH          .32608*   ‑.00935    ‑.31459*   ‑.10368     .08268     .15747

 TIME         ‑.31732*    .14655     .07322    ‑.02276    ‑.11320     .03428

 COG          ‑.28334*   ‑.01902     .17173     .14983    ‑.06110    ‑.12010

 DATA         ‑.15986    ‑.46128*    .36008    ‑.07347    ‑.14761     .06128

 LEARN        ‑.25227    ‑.38030*   ‑.03127     .34017*    .16834     .15273

 PARSI        ‑.03410    ‑.12764     .09310    ‑.00652    ‑.04193    ‑.04799

 INFLU         .22419     .10896     .57515*    .13349    ‑.29370    ‑.05110

 EARLY         .26233    ‑.04628    ‑.10997     .51862*    .03825     .27307

 SOCIAL       ‑.12369    ‑.12257     .03867     .49163*    .13589     .01540

 GOAL         ‑.20539     .14144     .25223     .30214*   ‑.06513     .00034

 VALUE        ‑.09861     .13987     .12987     .29536     .28964    ‑.26646

 AGREE        ‑.01220     .18610     .06580     .25217    ‑.14317     .12416

 GOOD         ‑.33015*    .36429*    .32580*    .29638     .44471*    .18545

 HERED         .04960    ‑.11310     .24118    ‑.18815     .36794*   ‑.06445

 PERCEP       ‑.23170     .20847     .00742     .19155    ‑.28685*   ‑.03778

 IMPOSE       ‑.14642     .12907     .00069     .13448    ‑.17966*    .01658

 THERA         .12568     .27235     .02229     .00194    ‑.45201*    .50039*

 

 

                       No. of    Predicted Group Membership

 

   Actual      1     2     3     4     5     6     7     8     9    10    11    12

 Freud      100.0    .0    .0    .0    .0    .0    .0    .0    .0    .0    .0    .0

 Adler         .0  58.8    .0  11.8    .0    .0  11.8  11.8    .0    .0    .0   5.9

 Jung          .0    .0 100.0    .0    .0    .0    .0    .0    .0    .0    .0    .0

 Rogers        .0    .0    .0  81.3    .0    .0    .0    .0    .0  12.5    .0   6.3

 Kelly         .0  11.8    .0   5.9  76.5    .0    .0    .0    .0    .0   5.9    .0

 Horney        .0    .0   6.7    .0   6.7  73.3   6.7    .0    .0    .0   6.7    .0

 Sulliva       .0  18.8  12.5    .0    .0  18.8  37.5    .0    .0    .0   6.3   6.3

 Bandura       .0   6.3    .0    .0  12.5    .0   6.3  75.0    .0    .0    .0    .0

 Cattell       .0    .0   6.7    .0    .0    .0    .0   6.7  86.7    .0    .0    .0

 Maslow        .0  11.8   5.9    .0    .0    .0    .0    .0    .0  76.5   5.9    .0

 Binswan       .0    .0    .0    .0    .0    .0    .0    .0    .0   6.7  93.3    .0

 Erikson       .0   8.3   8.3   8.3    .0    .0   8.3    .0    .0    .0    .0  66.7

 

 

Percent of "grouped" cases correctly classified:  77.25%

 

The Y-hat formula that was generated by these show that level of prediction of each of the categories or in this case the theorists.  That is, by knowing how the a theorist is rated on each of the items it can be predicted which theorists it is.  The level that each theorist is predicted is known.

Two sets of data from the output are useful in interpreting this data: (1) "Structure Matrix", and (2) the "Canonical Discriminant Functions evaluated and Group Means (Group Centroids)."  Plotting these two sets of data presents a pictures of the taxonomy of characteristics of variables and theorists.  It is necessary to first define the Structure Matrix and the Functions/Centroids.

The discriminant function is a prediction equation much like a in multiple regression.  The definition in chapter __ defines this general linear model.  In discriminant as set of predictor variables predicts a set of groups.  The first discriminant function seperates the groups most effectively and if the variables contain variance (information) such that the groups can be more accurately seperated a second discriminant function is computed and so on until there is no more variance among the groups that can be seperated by the variables.  The discriminant functions can be described by the variables that load on them in much the same manner as factor analysis.

The discriminant function can be used to make a prediction for each case.  When these cases are summed within each group and divided by the number of cases in that group these means are called centroids.  The greater difference among the means is the goal of discriminant function.  These means can be plotted to identify which functions are seperating which groups.  Further, when the functions are defined by the variable loadings then a taxonomy of the variables can be related to the groups.  In the case we are dealing with this means that the characteristics of a theory can be empirically related to the theory.

We arbitrarly requested 6 functions in the program (realizing that 9 function are significant) to demonstrate how the discriminant function can be interpreted.  Further we plot the group centroids to show their discriminating power for the various theorists.  We used only 3 2-way plots even though there is a possiblility of 15.  It does show the discriminating power of all 6 functions for all 12 theorists; it just does not show all combinations.  For example, it shows function 1 with function 2 but does not show function 1 with 3, 4, 5, or 6.  Although these might be interesting space does not allow presentation of all combinations.  The three presented should be useful in the interpretation ....  In fact, it might have been as useful to show the discriminating power for each of the functions independently.

The functions are also like the dimensions in multidimensional scaling, but are different in that there is a criterion variable in the discriminate function.  Further, the discriminant function allows ...  The graphs are created by using (1) "Structure Matrix", and (2) the "Canonical Discriminant Functions evaluated and Group Means (Group Centroids)" as mentioned above.  First the plots are created by using the data from the Group Centroids.  For example, notice in the first figure that Freud is to the far right with a score of 5.95 on Function 1.  Jung, Horney, Erikson, and Sullivan are near the center with scores of 1.03, .88, .31 and .37 respectively.  On Function 2 Rogers has the most positive score of 1.64 while Cattell has the most negative score of -2.65.  These functions are defined by the variables that correlate with them.  Function 1 is made up of Uncons, Consci, Drive, Active, Free, Hedon, Path, and Time.  Function 2 is made up of Data, Learn, and Good.

These functions can be interpreted like factors of factor analsysis.  The first function might be labeled "unconscious motivation" at one pole and conscious decision making at the other.  It is this that seperates Freud from most other theorists.  Kelly, Bandura, and Cattell are at the conscious decision making end of the continuum.  Function 2 is made up of Data, Learn, and Good.  Good is in the positive direction and Data and Learning are at the negative end of the function.  So that Rogers sees individuals as good, his theory is not based on empirical evidence and learning does not account for much of peoples' actions.  On the other hand, the theories of Cattell and Bandura data and learning have considerable impact on individuals but they are not seen as intrinsically good (one cannot conclude that they assume people are intrinsically bad).

 

 

 

 

 

 

 

In Figure __ Function 3 is not as clear Influ (influence), Data, Good, and Path (negative) do not seem to hang together very well.  However, they are the variables that seperate Horney and Binswanger from Rogers, Maslow and Cattell.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Seventy-seven percent correctly classified is decent prediction so that one would conclude that the instrument is reliable is distinguishing among different personality theories.  However, the instrument was not very effective in predicting Adler (58%) and Sullivan (37%), further Erikson with 67% could also be improved.  In diagnosing the problem it can be seen that the misses for Adler were with Rogers (12% misses for Adler were predicted to be Rogers), Sullivan, and Bandura (each with 12%).  One might hypothesize that the theory of Adler is similar to that of Rogers, Sullivan, and Bandura and it is not the problem with the measuring device.  Further, it might be hypothesized that Sullivan is similar to Adler, Jung, and Horney (19%, 13%, and 19% respectively).  This notion could be tested by combining the theories such that similar theorist would be in the same categories.  Another analysis was run with Adler and Sullivan combined into

a single category and the overall percentage of correct predictions went up slight to 79%.  The Adler Sullivan category was 54% correctly predicted, still somewhat low.  Further, this did not correct some of the overlap indicated.  It would be more advantages to see if there might be a way to separate the theorists.

The output from the first run indicates that there are more than 6 functions that are significant.  In fact there are 9 functions that are significant.  A jobstream was run requesting 9 functions and the percent correctly predicted rose to 85%. 


 

File Name = perdsc9.sps

 

get file = '\proeval\perall4.sav'/keep=

THID      CLUS      DRIVE    

GOAL      HEDON     COG       VALUE     ACTIVE    EARLY     IMPOSE    LEARN    

GOOD      HERED     CONSCI    UNCONS    SOCIAL    PERCEP    INFLU     TIME     

DATA      PARSI     FREE      THERA     PATH      AGREE .

value labels thid

      1 'freud'    

      2 'Adler'    

      3 'Jung'     

      4 'Rogers'   

      5 'Kelly'    

      6 'Horney'   

      7 'Sulliva'  

      8 'Bandura'  

      9 'Cattell'   

     10 'Maslow'   

     11 'Binswan'  

     12 'Erikson'.

missing values drive to agree (9).

DSC GROUPS=thid(1,12)

 /VAR=drive to agree 

 /METHOD=MINRESID 

 /PIN=.05    

 /FUNCTIONS=6,100,.05

 /STATISTICS=MEAN STDDEV COEFF RAW TABLE.

 

 

 

 

                      Canonical Discriminant Functions

 

                Pct of   Cum  Canonical  After  Wilks'

 Fcn Eigenvalue Variance  Pct     Corr      Fcn  Lambda  Chisquare    DF  Sig

                                         :    0   .0024   1014.589   198  .0000

   1*    4.9499   45.38   45.38    .9121 :    1   .0142    714.982   170  .0000

   2*    1.4590   13.38   58.76    .7703 :    2   .0349    563.823   144  .0000

   3*    1.3565   12.44   71.19    .7587 :    3   .0822    419.820   120  .0000

   4*     .8325    7.63   78.82    .6740 :    4   .1506    318.062    98  .0000

   5*     .7967    7.30   86.13    .6659 :    5   .2706    219.621    78  .0000

   6*     .5371    4.92   91.05    .5911 :    6   .4159    147.401    60  .0000

   7*     .2945    2.70   93.75    .4770 :    7   .5383    104.040    44  .0000

   8*     .2782    2.55   96.30    .4666 :    8   .6881     62.799    30  .0004

   9*     .1903    1.75   98.05    .3999 :    9   .8191     33.525    18  .0144

  10      .1662    1.52   99.57    .3775 :   10   .9552      7.693     8  .4640

  11      .0469     .43  100.00    .2116 :

 

 

Structure Matrix:

 

Pooled‑within‑groups correlations between discriminating variables

                                  and canonical discriminant functions

(Variables ordered by size of correlation within function)

 

             FUNC  1    FUNC  2    FUNC  3    FUNC  4    FUNC  5    FUNC  6

UNCONS        .48407*    .03096    ‑.09763    ‑.35571*    .26928     .43638*

CONSCI       ‑.44664*    .02689     .14508     .15771     .00853    ‑.08340

ACTIVE       ‑.41748*    .02171     .18051     .18981    ‑.10032    ‑.03243

FREE         ‑.37396*    .27632     .00144     .13380    ‑.16393    ‑.28372

HEDON         .33958*   ‑.05369    ‑.10844     .32823*    .00075    ‑.17824

TIME         ‑.31732*    .14655     .07322    ‑.02276    ‑.11320     .03428

COG          ‑.28334*   ‑.01902     .17173     .14983    ‑.06110    ‑.12010

DATA         ‑.15986    ‑.46128*    .36008*   ‑.07347    ‑.14761     .06128

LEARN        ‑.25227    ‑.38030*   ‑.03127     .34017*    .16834     .15273

INFLU         .22419     .10896     .57515*    .13349    ‑.29370    ‑.05110

EARLY         .26233    ‑.04628    ‑.10997     .51862*    .03825     .27307

SOCIAL       ‑.12369    ‑.12257     .03867     .49163*    .13589     .01540

VALUE        ‑.09861     .13987     .12987     .29536*    .28964    ‑.26646

AGREE        ‑.01220     .18610     .06580     .25217*   ‑.14317     .12416

GOOD         ‑.33015*    .36429*    .32580*    .29638*    .44471*    .18545

THERA         .12568     .27235     .02229     .00194    ‑.45201*    .50039*

GOAL         ‑.20539     .14144     .25223     .30214*   ‑.06513     .00034

DRIVE         .45355*    .01335     .05730    ‑.03132     .06143    ‑.32682*

PERCEP       ‑.23170     .20847     .00742     .19155    ‑.28685    ‑.03778

IMPOSE       ‑.14642     .12907     .00069     .13448    ‑.17966     .01658

HERED         .04960    ‑.11310     .24118    ‑.18815     .36794*   ‑.06445

PATH          .32608*   ‑.00935    ‑.31459*   ‑.10368     .08268     .15747

PARSI        ‑.03410    ‑.12764     .09310    ‑.00652    ‑.04193    ‑.04799

 

             FUNC  7    FUNC  8    FUNC  9

UNCONS       ‑.18115    ‑.00945     .01236

CONSCI        .09633    ‑.10474    ‑.17831

ACTIVE       ‑.02584    ‑.06411     .09399

FREE          .04931    ‑.09084     .30007*

HEDON         .10374     .22748     .11044

TIME          .08627     .02253     .03357

COG          ‑.01675    ‑.03132     .09982

DATA          .14982     .12043     .24718

LEARN         .26302     .08228     .29436

INFLU         .28069    ‑.17830     .17723

EARLY        ‑.06572    ‑.14613    ‑.15911

SOCIAL        .30753*   ‑.00789    ‑.23385

VALUE         .27222    ‑.24204    ‑.08582

AGREE        ‑.06715    ‑.04745     .24494

GOOD          .17276     .04759     .14258

THERA         .40108*    .05956    ‑.35879

GOAL         ‑.33333*    .09962    ‑.09469

DRIVE         .05246     .54241*   ‑.08198

PERCEP       ‑.02293     .47956*   ‑.08374

IMPOSE       ‑.08930     .19274*   ‑.12481

HERED        ‑.28983    ‑.07839    ‑.45725*

PATH          .27487     .15742    ‑.43764*

PARSI         .09651    ‑.03737     .25767*

 

Canonical Discriminant Functions evaluated at Group Means (Group Centroids)

 

  Group      FUNC   1    FUNC   2    FUNC   3    FUNC   4    FUNC   5

       1       5.95297      .15154      .28629      .05561    ‑1.15760

       2       ‑.63536     ‑.27522     ‑.00035     1.83737     ‑.15173

       3       1.02702     1.23000      .55006    ‑1.87012      .81240

       4      ‑1.46471     1.63556     1.68544      .26381     ‑.08564

       5      ‑2.42486      .46351     ‑.56310     ‑.62008    ‑1.47778

       6        .87926     ‑.12746    ‑2.36745      .13268     1.08705

       7        .37195     ‑.86906     ‑.85952      .27647      .40472

       8      ‑1.46161    ‑1.49840      .54719      .30448     ‑.86419

       9       ‑.59271    ‑2.65032     1.03258    ‑1.18762      .46617

      10       ‑.35662      .98185      .87905      .46556      .93586

      11      ‑1.59251      .96399    ‑1.73615     ‑.52494     ‑.44835

      12        .31087     ‑.05714      .48770      .58778     1.10934

 

  Group      FUNC   6    FUNC   7    FUNC   8    FUNC   9

       1       ‑.26492     ‑.06609      .05194      .02423

       2        .35772     ‑.65579     ‑.38601     ‑.62244

       3        .83661      .03531     ‑.61179     ‑.22382

       4        .56233      .49353      .17086     ‑.14415

       5        .58221     ‑.69567      .57408      .29868

       6        .63629     ‑.19940     ‑.22853      .54813

       7        .35528      .97323     1.08427     ‑.31534

       8        .01865      .78145     ‑.79608      .61210

       9       ‑.44479     ‑.50719      .17872     ‑.29761

      10      ‑1.26531     ‑.27827      .38276      .59534

      11      ‑1.41790      .32617     ‑.40514     ‑.55439

      12        .27400     ‑.13150     ‑.20468     ‑.07838

 

Classification Results ‑

 

                      No. of    Predicted Group Membership

   Actual     1     2     3     4     5     6     7     8     9    10    11    12

 

Freud     100.0    .0    .0    .0    .0    .0    .0    .0    .0    .0    .0    .0

Adler        .0  70.6    .0   5.9   5.9    .0    .0    .0    .0   5.9    .0  11.8

Jung         .0    .0  93.8    .0    .0    .0    .0    .0    .0    .0    .0   6.3

Rogers       .0    .0    .0 100.0    .0    .0    .0    .0    .0    .0    .0    .0

Kelly        .0   5.9    .0  11.8  76.5    .0    .0   5.9    .0    .0    .0    .0

Horney       .0    .0    .0    .0   6.7  86.7   6.7    .0    .0    .0    .0    .0

Sulliva      .0    .0  12.5    .0    .0  18.8  56.3    .0    .0    .0    .0  12.5

Bandura      .0    .0    .0    .0   6.3    .0    .0  93.8    .0    .0    .0    .0

Cattell      .0    .0    .0    .0    .0    .0   6.7    .0  93.3    .0    .0    .0

Maslow       .0   5.9   5.9   5.9    .0    .0    .0    .0    .0  70.6  11.8    .0

Binswan      .0    .0    .0    .0    .0    .0    .0    .0    .0    .0 100.0    .0

Erikson      .0   8.3    .0   8.3    .0    .0    .0    .0    .0    .0    .0  83.3

 

 

Eighty-Five of the cases were correctly classified.  This represents an improvement over the previous run where 77% of cases were correctly classified.  It was noted above the that the 6 function solution did not discriminate well on the theorists Adler, Jung, Rogers, Horney, Sullivan, Bandura, and Erikson.  Figures __ and __ demonstrate that Functions 7, 8, and 9 performed that task.  Figure __ shows Functions 7 and 8; on Function 7 Sullivan and Bandura are on one

end of the continuum and Kelly and Adler at the other end of the continuum.  Further, Erikson and Horney are to the left while Rogers is to the right.  Function 8 seperates Sullivan and Kelly from Erikson, Horney, Adler, Jung and Bandura.  And finally Function 9 seperates Adler and Sullivan from Bandura and Horney.