concept mapping: an introduction to structured conceptualization william trochim cornell university

Concept Mapping: An Introduction to

StructuredConceptualization

William TrochimCornell University

What is concept mapping?

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

A method that...

In about 4 hours of participant time a group can...

...Brainstorm a large set of issues...

• innovations in way network is delivered• (investigate) corporate/structural alignment• assist in the development of non-traditional partnerships (Rehab with

the Medicine Community)• expand investigation and knowledge of PSN'S/PSO's• continue STHCS sponsored forums on public health issues (medicine

managed care forum)• inventory assets of all participating agencies (providers, Venn

Diagrams)• access additional funds for telemedicine expansion • better utilization of current technological bridge• continued support by STHCS to member facilities• expand and encourage utilization of interface programs to strengthen

the viability and to improve the health care delivery system (ie teleconference)

• discussion with CCHN

• innovations in way network is delivered• (investigate) corporate/structural alignment• assist in the development of non-traditional partnerships (Rehab with the

Medicine Community)• expand investigation and knowledge of PSN'S/PSO's• continue STHCS sponsored forums on public health issues (medicine

managed care forum)• inventory assets of all participating agencies (providers, Venn Diagrams)• access additional funds for telemedicine expansion • better utilization of current technological bridge• continued support by STHCS to member facilities• expand and encourage utilization of interface programs to strengthen the

viability and to improve the health care delivery system (ie teleconference)• discussion with CCHN

...organize the issues...

brainstorm

Work quickly and effectively

under pressure

49

Organize the work when

directions are not specific.

39

Decide how to manage

multiple tasks.20 Manage resources effectively.

4

sort

12

34

5

12

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5

3Scan a multitu

de of inform

ation

and decide what is im

portant.

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1Manage tim

e effectively

2Manage resources effectively.

3Scan a multitu

de of

information and decide what is

important.

4Decide how to manage multip

le tasks.

5Organize the work when directions are not specific

.

1Manage tim

e effectively

Rating Sheet

rate





Work quickly and effectively under

pressure49

Organize the work when directions are not

specific.39

Decide how to manage multiple tasks.

20

Manage resources effectively.4

sort

12

34

5

12

34

5

3Scan a

multitude o

f inform

ation and

decide what is im

portant.12

34

5

12

34

5

12

34

5

12

34

5

12

34

5

1Manage tim

e effectively

2Manage resources eff

ectively.

3Scan a multitu

de of inform

ation and

decide what is important.


le tasks.

5Organize the work w

hen directions are not specific

.

1Manage tim

e effectively

Rating Sheet

rate

brainstorm

organize

Management

Financing

Regionalization

STHCS as model

Community & Consumer Views

Information ServicesTechnology

…”map” the issues...

Financing STHCS as model

Technology

Management

Regionalization


Information Services

• better utilization of current technological bridge (8)• expand and encourage utilization of interface programs to strengthen

the viability and to improve the health care delivery system (ie teleconference) (10)

• patient information system to be shared by all members (19)• the STHCS will assess the status of all participant organization interface

technology development and needs (20)• teleconference board meeting (21)• development of interface technology (30)• continued advancement of tech interface (44)• assure 100% board member access to wide area network (46)• utilize the televideo telecommunication, telemedicine to share

resources/strengths (50)• establishment of a virtual network -- as an intranet originally and

eventually an internet solution (61)

ManagementFinancing

Regionalization

Mission & Ideology


Information Services Technology






pressure49


specific.39


20


sort

12

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3Scan a

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ectively.

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le tasks.



.

1Manage tim

e effectively

Rating Sheet

rate

brainstorm

organize

Management

Financing

Regionalization

STHCS as model



map

...prioritize the issues......prioritize the issues...

ManagementFinancing

Regionalization

Mission & Ideology


Information Services Technology






pressure49


specific.39


20


sort

12

34

5

12

34

5

3Scan a

multitude o

f inform

ation and

decide what is im

portant.12

34

5

12

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5

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12

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1Manage tim

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ectively.

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le tasks.



.

1Manage tim

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Rating Sheet

rate

brainstorm

organize

Management

Financing

Regionalization

STHCS as model



mapr = .72

Counties 1 & 2 County 3

4.23

3.55

4.4

3.56


Management


Regionalization

Technology

Financing

Mission & Ideology

Technology



Management

Regionalization

Financing

Mission & Ideology

...examine consensus...

prioritize

r = .72

4.23

3.55

4.4

3.56






pressure49


specific.39


20


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1Manage tim

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Rating Sheet

rate

brainstorm

organize

Management

Financing

Regionalization

STHCS as model



map

ManagementFinancing

Regionalization

Mission & Ideology


Information Services Technologyprioritize

2.471.24.8

1.8

5

Importance

Feasib

ilit

y

2.6

1

101722

25

33

34 37

4562

75

76

…and “drill back down” to details for prioritizing action

CConcept MMapping (Sorting input)

To To organizeorganize the issuesthe issues

CConcept MMapping (Sorting input)

To To organizeorganize the issuesthe issues

Concept Mapping Process

MMeasurement (Rating input)

To To observe observe expectations and resultsexpectations and results

PPattern MMatching and Go Zones

To To linklink expectations and results, importance and capacityexpectations and results, importance and capacity

PPattern MMatching and Go Zones

To To linklink expectations and results, importance and capacityexpectations and results, importance and capacity

Concept Mapping to organize

• identify group shared vision• represent group ideas

pictorially• encourage teamwork• facilitate group decision making

Uses information from Uses information from individualsindividuals to: to:

...focus

1. Prepare Project: Develop a focus

“A specific issue that is relevant to the mental health of women and girls is . . ."

“A specific issue that is relevant to the mental health of women and girls is . . ."

To begin…To begin…

Participants Contribute Knowledge and OpinionParticipants 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)

• 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

Participants Build the Conceptual FrameworkParticipants Build the Conceptual Framework

1. Prepare Projectsort

2. Generate Ideas

3. Structure Ideas

12

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5Organize the work when directions are not

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1Manage tim

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Rating Sheet

12

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12

34

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3Scan a multitu

de of inform

ation


portant.

12

34

5

12

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12

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12

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de of


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specific.

1Manage tim

e effectively

Rating Sheet

rate

Work quickly

and effectively

underOrganize the work

when directions

are not specific.

39

Decide how to

manage multiple tasks.

20 Manage resources effectively.

4

12

34

5

12

34

5

3Scan a multitu

de of inform

ation


portant.

12

34

5

12

34

5

12

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5

12

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5

12

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5

1Manage tim

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1Manage tim

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Rating Sheet

12

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12

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Rating Sheet

The Process Turns Knowledge into DataThe Process Turns Knowledge into Data

3. Structure Ideas

2. Generate Ideas

1. Prepare Project

4. Compute Maps

r = .51

Area 1 Area 2

4.22

3.47

4.4

3.56

Community & Consumer

Management


Regionalization

Technology

Financing

Mission & Ideology

Technology

Community & Consumer


Management

Regionalization

Financing

Mission & Ideology

Management

Financing

Regionalization

Mission &

Ideology



Technology

And Data Into MeaningAnd Data Into Meaning

Management

ChangeControl

Client Issues

Team IssuesPersonal Awareness& Skill

Graphical User

Interface

TechnicalIssues

Processes/Methodology

Documentation

5. Interpret Maps

4. Compute Maps

3. Structure Ideas

2. Generate Ideas

1. Prepare Project

Meaning Into Action, Policy, and EvaluationMeaning Into Action, Policy, and Evaluation

5. Interpret Maps

4. Compute Maps

3. Structure Ideas

2. Generate Ideas

1. Prepare Project

6. Utilize Maps

r = .51

Area 1 Area 2

4.22

3.47

4.4

3.56


Management


Regionalization

Technology

Financing

Mission & Ideology

Technology



Management

Regionalization

Financing

Mission & Ideology

The emerging structure…The emerging structure…The emerging structure…The emerging structure…

…contains all the details and provides a conceptual framework.

Capacity of Community Services

GerotechnologyImpairments

Housing Continuum

EconomicSecurity

Access to Benefits

Communication

AttitudesTowards

Aging

Special Needs & Mental Health

Transportation

Workforce

Caregiving

EngagedLifestyle

• 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

How Did We Build These Results?

Binary, square similarity matrix

Sort for one participant

Representation

Total square similarity matrix

across participants

Multidimensional Scaling

Output: An n-dimensional mapping of the entities

5655

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Input: A square matrix of relationships among a set of entities

5 1 2 4 0 1 1 3 1 01 5 0 0 0 1 0 0 2 02 0 5 3 0 0 0 0 0 04 0 3 5 0 0 0 0 0 00 0 0 0 5 0 0 2 0 01 1 0 0 0 5 0 0 4 01 0 0 0 0 0 5 0 0 03 0 0 0 2 0 0 5 0 01 2 0 0 0 4 0 0 5 00 0 0 0 0 0 0 0 0 5


1 2 31 5 1 22 1 5 03 2 0 5

1

If 4 out of 5 people grouped statement 1 with 2





Similarity Matrix


1 2 31 5 1 22 1 5 03 2 0 5

1

2

Similarity Matrix


1 2 31 5 1 22 1 5 03 2 0 5

1

2

3

3

Similarity Matrix

1 2 3 41 5 1 2 42 1 5 0 03 2 0 5 34 4 0 3 5


23

14

Similarity Matrix

1 2 3 41 5 1 2 42 1 5 0 03 2 0 5 34 4 0 3 5


A map can be depicted as a

coordinate matrix

23

41

x

y

Similarity Matrix

x y1 2.8 1.02 5.9 3.23 1.1 3.24 1.9 1.3

CoordinateMatrix

1 2 3 41 5 1 2 42 1 5 0 03 2 0 5 34 4 0 3 5


23

4


coordinate matrix 1

x

y

Similarity Matrix

x y1 2.8 1.02 5.9 3.23 1.1 3.24 1.9 1.3

CoordinateMatrix

And from the coordinates we can

compute the distances between all pairs of points

2

1a

bc

a2 + b2 = c2

a = difference between x valuesb = difference between y valuesc = distance

1 2 3 41 5 1 2 42 1 5 0 03 2 0 5 34 4 0 3 5


23

4


coordinate matrix 1

x

y

Similarity Matrix

x y1 2.8 1.02 5.9 3.23 1.1 3.24 1.9 1.3

CoordinateMatrix

And can show these as a matrix

of distances between points

1 2 3 41 0.0 3.2 2.8 1.12 3.2 0.0 4.8 4.63 2.8 4.8 0.0 2.14 1.1 4.6 2.1 0.0

Distance Matrix



a2 + b2 = c2


StressIs the relationship

between the similarity input matrix and the

distances on the map

1 2 3 41 5 1 2 42 1 5 0 03 2 0 5 34 4 0 3 5


23

4


coordinate matrix 1

x

y

Similarity Matrix

x y1 2.8 1.02 5.9 3.23 1.1 3.24 1.9 1.3

CoordinateMatrix

And can show these as a matrix

of distances between points

1 2 3 41 0.0 3.2 2.8 1.12 3.2 0.0 4.8 4.63 2.8 4.8 0.0 2.14 1.1 4.6 2.1 0.0

Distance Matrix



a2 + b2 = c2


StressIs the relationship

between the similarity input matrix and the

distances on the map

1 2 3 41 5 1 2 42 1 5 0 03 2 0 5 34 4 0 3 5


Similarity Matrix

1 2 3 41 0.0 3.2 2.8 1.12 3.2 0.0 4.8 4.63 2.8 4.8 0.0 2.14 1.1 4.6 2.1 0.0

Distance Matrix

1,1 51,2 11,3 21,4 42,2 52,3 02,4 03,3 53,4 34,4 5

1,1 0.01,2 3.21,3 2.81,4 1.12,2 0.02,3 4.82,4 4.63,3 0.03,4 2.14,4 0.0

Similarities Distances

Low stress values means there is a

greater correspondence

between the similarities and the

map


• Directionality– Does MDS know North from

South?

• Dimensionality– Why only two dimensions?

• Stress– How much does it really matter?

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– Ward’s algorithm

• Number of Clusters

Cluster Analysis

16

8

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1 6 8 3 4 7 5 9 10 2

10987654321

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Merge Points Merged

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Cluster Analysis

1 6 8 3 4 7 5 9 10 2

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Merge Points Merged

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Cluster Analysis

1 6 8 3 4 7 5 9 10 2

10987654321

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1 + 65 + 7

Merge Points Merged

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Cluster Analysis

1 6 8 3 4 7 5 9 10 2

10987654321

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1 + 65 + 79 + 10

Merge Points Merged

123

Cluster Analysis

1 6 8 3 4 7 5 9 10 2

10987654321

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1 + 65 + 79 + 10(1 + 6) + 8

Merge Points Merged

1234

Cluster Analysis

1 6 8 3 4 7 5 9 10 2

10987654321

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lust

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1 + 65 + 79 + 10(1 + 6) + 83 + 4

Merge Points Merged

12345

Cluster Analysis

1 6 8 3 4 7 5 9 10 2

10987654321

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lust

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1 + 65 + 79 + 10(1 + 6) + 83 + 42 + (9 + 10)

Merge Points Merged

123456

Cluster Analysis

1 6 8 3 4 7 5 9 10 2

10987654321

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lust

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1 + 65 + 79 + 10(1 + 6) + 83 + 42 + (9 + 10)((1 + 6) + 8)) + (3 + 4)

Merge Points Merged

1234567

Cluster Analysis

1 6 8 3 4 7 5 9 10 2

10987654321

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f C

lust

ers

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1 + 65 + 79 + 10(1 + 6) + 83 + 42 + (9 + 10)((1 + 6) + 8)) + (3 + 4) (5 + 7) + ((2 + (9 + 10))

Merge Points Merged

12345678

1 + 65 + 79 + 10(1 + 6) + 83 + 42 + (9 + 10)((1 + 6) + 8)) + (3 + 4) (5 + 7) + ((2 + (9 + 10))(((1 + 6) + 8)) + (3 + 4)) + (5 + 7) + ((2 + (9 + 10))

Cluster Analysis

1 6 8 3 4 7 5 9 10 2

10987654321

Nu

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lust

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Merge Points Merged

123456789

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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.

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

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.

Bridging Value, Step 1

1. We begin by computing the proportion of sorters who put point i and j together in a pile:

m

sp ij

ij

where sij = number of sorters who placed point i and j together in

the same pilem = total number of sorterspij = proportion of sorters who placed point i and j together

in the same pile


2. We compute the Euclidean Distance between all pairs of standardized points:

22 )()( jijiij yyxxd

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


3. We compute the unstandardized bridging value:

n

jn

jij

ijiji

p

dp

1

1

)*(b

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


4. Normalize the bridging raw value:

)min()max(

)min(b

bb

bb i

i

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

Sort Pile Label Analysis

• finds the “best fitting” sort pile label for a cluster

• done after the map is computed• based on centroid computations

50

43

41

37

36

3

Sort Pile Label AnalysisSort Pile Label AnalysisWhat is a centroid?

X

Y

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41

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36

3

Sort Pile Label AnalysisSort Pile Label AnalysisWhat is a centroid?

Average X

Av

era

ge

Y

X

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29

16133

36

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Sort Pile Label AnalysisSort Pile Label Analysis

xx

Your Pile:

50, 36, 43, 3,13, 16, 29

5043

29

16133

36

ClusterCentroid Pile

Centroid

distance

• 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

Sort Pile Label AnalysisSort Pile Label Analysis

Cluster Map with Labels

Capacity of Community Services


Housing Continuum

Economic Security

Access to Benefits

Communication

Engaged Lifestyle

Attitudes Towards Aging

Special Needs & Mental Health

Transportation

Workforce

Caregiving

Importance

Layer Value 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

Capacity ofCommunity Services


HousingContinuum

EconomicSecurity

Access toBenefits

Communication

Engaged Lifestyle

Workforce

Caregiving

Transportation

Special Needs& Mental Health


Feasibility



Housing Continuum

EconomicSecurity

Access toBenefits

Communication

Engaged Lifestyle

Caregiving

Transportation

Workforce



AttitudesTowards

Aging

Importance

Importance 4.46

3.62

Engaged Lifestyle

Gerotechnology


Special Needs & Mental HealthHousing Continuum

CommunicationCaregiving

ImpairmentsCapacity of Community Services

WorkforceTransportation

Access to Benefits

Economic Security




HousingContinuum

EconomicSecurity

Access toBenefits

Communication

Engaged Lifestyle

Workforce

Caregiving

Transportation



Feasibility

Feasibility

3.59

2.98

Economic Security

Access to BenefitsHousing ContinuumCaregiving

WorkforceGerotechnologyAttitudes Towards AgingCapacity of Community ServicesSpecial Needs & Mental HealthImpairmentsEngaged Lifestyle

Transportation

Communication



Housing Continuum

EconomicSecurity

Access toBenefits

Communication

Engaged Lifestyle

Caregiving

Transportation

Workforce



AttitudesTowards

Aging

Importance vs. Feasibility

r = -.27

Importance Feasibility 4.46

3.62

3.59

2.98

Economic Security

Access to BenefitsHousing ContinuumCaregiving

WorkforceGerotechnologyAttitudes Towards AgingCapacity of Community ServicesSpecial Needs & Mental HealthImpairmentsEngaged Lifestyle

Transportation

Engaged Lifestyle

Gerotechnology


Special Needs & Mental HealthHousing Continuum

CommunicationCaregiving

ImpairmentsCapacity of Community Services

WorkforceTransportation

Access to Benefits

Economic Security Communication

Comparing each Unique Statement on Importance and Feasibility: Go Zones

the number of senior communitycenters in outer boroughs andtheir ability to handle influx (1)

1

2

homecare services during holidays and vacations (2)

3

affordable opportunities for recreation / entertainment/ socialization for seniors, including access to fitness and wellness programs (3)

4 research funding for Alzheimer's (4)

Cluster mean of each scale is used to

divide the matrix

Feasi

bili

ty

Low

High

ImportanceLow High

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

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

concept mapping: an introduction to structured conceptualization william trochim cornell university

Documents

medicine community

multitude of information

health care delivery

sthcs sponsored forums

way network

cchn slide

patient information

cchn work