The CPM Model for Planning and Evaluation

1
Concept Mapping An Introduction
to Structured Conceptualization William
Trochim Cornell University
2
What is concept mapping?
A method that...

• Focuses and helps objectify the group planning
  process
• Helps individuals think as a group...
• ...without losing their individuality
• Helps groups to manage complexity...
• ...without trivializing or losing detail

3
In about 4 hours of participant time a group
can...
...Brainstorm a large set of issues...
4
brainstorm
...organize the issues...
5
brainstorm
map the issues...
organize
6
Technology
Financing
STHCS as model
7
brainstorm
organize
map
...prioritize the issues...
8
brainstorm
organize
map
prioritize
...examine consensus...
9
brainstorm
organize
map
and drill back down to details for
prioritizing action
prioritize
10
Concept Mapping Process
11
Concept Mapping to organize
Uses information from individuals to

• identify group shared vision
• represent group ideas pictorially
• encourage teamwork
• facilitate group decision making

12
To begin
1. Prepare Project Develop a focus
A specific issue that is relevant to the mental
health of women and girls is . . ."
...focus
13
Participants Contribute Knowledge and Opinion
1. Prepare Project

• Body image issues- (breast size, hair
  color/texture, nose, other physical features vs
  external valuation of "beauty"). (9)
• The development and evaluation of Internet-based
  interventions that can be accessed by women
  anywhere, anytime. (31)
• The impact of race, ethnicity, culture, class,
  sexual orientation and age on the expression of
  symptoms. (54)
• Lack of encouragement and opportunity at the
  elementary, middle and high school levels for
  career opportunities that girls can aspire to.
  (61)
• Lack of parity for mental health care coverage.
  (102)

2. Generate Ideas
14
Participants Build the Conceptual Framework
1. Prepare Project
sort
Decide how to manage multiple tasks. 20
Manage resources effectively. 4
Work quickly and effectively under
2. Generate Ideas
Organize the work when directions are not
specific. 39
3. Structure Ideas
rate
15
The Process Turns Knowledge into Data
1. Prepare Project
2. Generate Ideas
3. Structure Ideas
4. Compute Maps
16
And Data Into Meaning
1. Prepare Project
Technical Issues
Graphical User
Interface
Documentation
Client Issues
Change
Control
Personal Awareness
Team Issues
Skill
Management
2. Generate Ideas
5. Interpret Maps
3. Structure Ideas
4. Compute Maps
17
Meaning Into Action, Policy, and Evaluation
1. Prepare Project
2. Generate Ideas
6. Utilize Maps
5. Interpret Maps
3. Structure Ideas
4. Compute Maps
18
The emerging structure
Housing Continuum
Workforce
Transportation
Capacity of Community Services
Caregiving
Special Needs Mental Health
Access to Benefits
Gerotechnology
Communication
Impairments
Economic Security
Attitudes Towards Aging
Engaged Lifestyle
contains all the details and provides a
conceptual framework.
19
How Did We Build These Results?

• The Raw Materials
• Statements
• Sort Input from each participant
• The Tools
• Aggregation of Sort Data
• Similarity Matrix
• Multidimensional Scaling
• Hierarchical cluster analysis
• Anchoring/Bridging Analysis

20
Representation
21
Multidimensional Scaling
22
Multidimensional Scaling
Similarity Matrix
1 2 3 1 5 1 2 2 1 5 0 3 2 0 5
23
Multidimensional Scaling
Similarity Matrix
1 2 3 1 5 1 2 2 1 5 0 3 2 0 5
1
24
Multidimensional Scaling
Similarity Matrix
1 2 3 1 5 1 2 2 1 5 0 3 2 0 5
2
1
25
Multidimensional Scaling
Similarity Matrix
1 2 3 4 1 5 1 2 4 2 1 5 0 0 3 2 0 5 3 4 4 0 3 5
2
3
1
26
Multidimensional Scaling
Similarity Matrix
1 2 3 4 1 5 1 2 4 2 1 5 0 0 3 2 0 5 3 4 4 0 3 5
A map can be depicted as a coordinate matrix
27
Multidimensional Scaling
Similarity Matrix
1 2 3 4 1 5 1 2 4 2 1 5 0 0 3 2 0 5 3 4 4 0 3 5
y
2
3
A map can be depicted as a coordinate matrix
1
x
And from the coordinates we can compute the
distances between all pairs of points
a2 b2 c2
a difference between x values b difference
between y values c distance
28
Multidimensional Scaling
Similarity Matrix
1 2 3 4 1 5 1 2 4 2 1 5 0 0 3 2 0 5 3 4 4 0 3 5
y
2
3
And can show these as a matrix of distances
between points
A map can be depicted as a coordinate matrix
1
x
And from the coordinates we can compute the
distances between all pairs of points
a2 b2 c2
a difference between x values b difference
between y values c distance
29
Multidimensional Scaling
Similarity Matrix
1 2 3 4 1 5 1 2 4 2 1 5 0 0 3 2 0 5 3 4 4 0 3 5
y
2
3
And can show these as a matrix of distances
between points
A map can be depicted as a coordinate matrix
1
x
And from the coordinates we can compute the
distances between all pairs of points
a2 b2 c2
a difference between x values b difference
between y values c distance
30
Multidimensional Scaling
Similarity Matrix
1 2 3 4 1 5 1 2 4 2 1 5 0 0 3 2 0 5 3 4 4 0 3 5
Low stress values means there is a greater
correspondence between the similarities and the
map
31
Multidimensional Scaling

• Directionality
• Does MDS know North from South?
• Dimensionality
• Why only two dimensions?
• Stress
• How much does it really matter?

32
Cluster Analysis

• Hierarchical
• clusters get built in a tree-like method
• Agglomerative
• builds toward all items in one pile (divisive -
  all start in one and divide)
• Clustering criterion
• the rule used to decide the next cluster merge
• Wards algorithm
• Number of Clusters

33
Cluster Analysis
7
5
8
9
10
1
6
2
3
4
Merge
Points Merged
1
34
Cluster Analysis
7
5
8
9
10
1
6
2
3
4
Merge
Points Merged

1 6
1
35
Cluster Analysis
7
5
8
9
10
1
6
2
3
4
Merge
Points Merged
1 6 5 7
1 2
36
Cluster Analysis
7
5
8
9
10
1
6
2
3
4
Merge
Points Merged
1 6 5 7 9 10
1 2 3
37
Cluster Analysis
7
5
8
9
10
1
6
2
3
4
Merge
Points Merged
1 6 5 7 9 10 (1 6) 8
1 2 3 4
38
Cluster Analysis
7
5
8
9
10
1
6
2
3
4
Merge
Points Merged
1 6 5 7 9 10 (1 6) 8 3 4
1 2 3 4 5
39
Cluster Analysis
7
5
8
9
10
1
6
2
3
4
Merge
Points Merged
1 6 5 7 9 10 (1 6) 8 3 4 2 (9 10)
1 2 3 4 5 6
40
Cluster Analysis
7
5
8
9
10
1
6
2
3
4
Merge
Points Merged
1 6 5 7 9 10 (1 6) 8 3 4 2 (9
10) ((1 6) 8)) (3 4)
1 2 3 4 5 6 7
41
Cluster Analysis
7
5
8
9
10
1
6
2
3
4
Merge
Points Merged
1 6 5 7 9 10 (1 6) 8 3 4 2 (9
10) ((1 6) 8)) (3 4) (5 7) ((2 (9
10))
1 2 3 4 5 6 7 8
42
Cluster Analysis
7
5
8
9
10
1
6
2
3
4
Merge
Points Merged
1 6 5 7 9 10 (1 6) 8 3 4 2 (9
10) ((1 6) 8)) (3 4) (5 7) ((2 (9
10)) (((1 6) 8)) (3 4)) (5 7)
((2 (9 10))
1 2 3 4 5 6 7 8 9
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What is the Bridging Value?

• tells you whether the statement was sorted with
  others that are close to it on the map or whether
  it was sorted with items that are farther away on
  the map.

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The Bridging Value

• Helps us interpret what content is associated
  with specific areas of the map
• Statements with lower bridging values are
  generally better indicators of the meaning of
  their part of the map than statements with higher
  bridging values
• Statements with higher bridging values means
  statement is a bridge between different areas on
  map

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Compute Bridging Values

• A bridging value always ranges from 0 to 1
• The bridging values are computed after the map is
  computed.
• The cluster bridging value is simply the average
  bridging value across all statements in a cluster.

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Bridging Value, Step 1
1. We begin by computing the proportion of
sorters who put point i and j together in a pile
where sij number of sorters who placed point i
and j together in the same pile m total number
of sorters pij proportion of sorters who placed
point i and j together in the same pile
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Bridging Value, Step 2
2. We compute the Euclidean Distance between all
pairs of standardized points
Where xi MDS x-coordinate for point i yi MDS
y-coordinate for point i xj MDS x-coordinate
for point j yj MDS y-coordinate for point j dij
standardized Euclidean Distance between points
i and j
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Bridging Value, Step 3
3. We compute the unstandardized bridging value
where bi bridging raw value for point i pij
proportion of sorters who placed point i and j
together in the same pile dij standardized
Euclidean Distance between points i and j
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Bridging Value, Step 4
4. Normalize the bridging raw value
Where bi bridging raw value for point
i min(b) minimum of the bi values
max(b) maximum of the bi values bi
standardized bridging value
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Sort Pile Label Analysis

• finds the best fitting sort pile label for a
  cluster
• done after the map is computed
• based on centroid computations

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Sort Pile Label Analysis
What is a centroid?
Y
X
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Sort Pile Label Analysis
What is a centroid?
Y
X
53
Sort Pile Label Analysis
What is a centroid?
Average Y
Average X
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Sort Pile Label Analysis
2
18
24
38
23
17
27
26
22
12
8
52
25
x
44
x
6
37
41
30
34
7
35
51
47
42
31
10
33
54
45
28
32
14
39
1
40
11
46
49
48
4
9
56
19
20
55
21
5
53
15
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Sort Pile Label Analysis

• Every cluster has a centroid
• Every sort pile has a centroid
• the average x,y for all items in the pile
• this is the best location on the map for the pile
  label
• can compute the distance between this label and
  any other point on the map
• For each cluster
• compare distance between its centroid and each
  sort pile centroid
• best sort pile label is the closest one

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Cluster Map with Labels
Housing Continuum
Workforce
Transportation
Capacity of Community Services
Caregiving
Special Needs Mental Health
Access to Benefits
Gerotechnology
Impairments
Economic Security
Communication
Attitudes Towards Aging
Engaged Lifestyle
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Importance
Housing Continuum
Workforce
Capacity of Community Services
Transportation
Access to Benefits
Caregiving
Special Needs Mental Health
Communication
Gerotechnology
Impairments
Attitudes Towards Aging
Economic Security
Layer Value
Engaged Lifestyle
1 3.62 to 3.79
2 3.79 to 3.95
3 3.95 to 4.12
4 4.12 to 4.29
5 4.29 to 4.46
58
Feasibility
Housing Continuum
Workforce
Transportation
Capacity of Community Services
Caregiving
Access to Benefits
Special Needs Mental Health
Communication
Gerotechnology
Impairments
Attitudes Towards Aging
Economic Security
Layer Value
Engaged Lifestyle
1 2.98 to 3.11
2 3.11 to 3.23
3 3.23 to 3.35
4 3.35 to 3.47
5 3.47 to 3.59
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Importance
Importance
4.46
Economic Security
Access to Benefits
Transportation
Workforce
Capacity of Community Services
Impairments
Caregiving
Communication
Housing Continuum
Special Needs Mental Health
Attitudes Towards Aging
Gerotechnology
Engaged Lifestyle
3.62
60
Feasibility
Feasibility
3.59
Communication
Transportation
Engaged Lifestyle
Impairments
Special Needs Mental Health
Capacity of Community Services
Attitudes Towards Aging
Gerotechnology
Workforce
Caregiving
Housing Continuum
Access to Benefits
Economic Security
2.98
61
Importance vs. Feasibility
Importance
Feasibility
4.46
3.59
Economic Security
Communication
Access to Benefits
Transportation
Workforce
Capacity of Community Services
Impairments
Transportation
Caregiving
Communication
Engaged Lifestyle
Housing Continuum
Impairments
Special Needs Mental Health
Special Needs Mental Health
Capacity of Community Services
Attitudes Towards Aging
Attitudes Towards Aging
Gerotechnology
Workforce
Caregiving
Gerotechnology
Housing Continuum
Access to Benefits
Engaged Lifestyle
Economic Security
r -.27
3.62
2.98
62
Comparing each Unique Statement on Importance and
Feasibility Go Zones
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Features of Concept Mapping

• guides project throughout life-cycle - beginning
  to end
• involves many stakeholder groups throughout the
  entire training life-cycle
• easily scalable and transferable
• uses state-of-the-art analytical tools to provide
  rigor and credibility

64
Benefits of Concept Mapping

• visual product is easy to understand and present
• identifies disconnects before significant
  investments are made
• offers significant cost savings while improving
  the quality of project