basics of causal loop diagrams - welcome to the department of
TRANSCRIPT
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Basics of Causal Loop
Diagrams
CMPT 858
Nathaniel Osgood
1/25/2011
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Causal Loop Diagram
• Focuses on capturing causality – and
especially feedback effects
• Indicates sign of causal impact (+ vs. –)
– x →+y indicates
– x →-y indicates
0y
x
0y
x
Hunger
Food Ingested
+-
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Causal Loop Diagram
– An arrow with a positive sign (+): “all
else remaining equal, an increase
(decrease) in the first variable
increases (decreases) the second
variable above (below) what it would otherwise have been.”
– An arrow with a negative sign (-): “all
else remaining equal, an increase
(decrease) in the first variable
decreases (increases) the second
variable below (above) what it otherwise would have been.”
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Reasoning about Link Polarity • Easy to get confused regarding link polarity
in the context of a causal pathway
• Tips for reasoning about X→Y link polarity
– Reason about this link in isolation
• Do not be concerned about links preceding X or
following Y
– Ask “if X were to INCREASE, would Y increase
or decrease compared to what it would otherwise have been”?
• Increase in Y implies “+”,decrease in Y implies “-”
• If answer is not clear or depends on value of X, need
to think about representing several paths between X
and Y
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Consider A → B
• We are reasoning here about causal influences – The changes on B caused by changes in A • This is not merely an associational relationship
• This should not merely be a matter of definition
• Notion of “Increase” • Must Clearly Distinguish
– “if X were to INCREASE, would Y increase or decrease compared to what it would have otherwise been ”?
• “if X were to INCREASE, would Y increase or decrease over time”? – i.e. “if X were to INCREASE, would Y rise or fall over time”?
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Reminder – An arrow with a positive sign (+): “all
else remaining equal, an increase (decrease) in the first variable increases (decreases) the second variable above (below) what it would otherwise have been.”
– An arrow with a negative sign (-): “all else remaining equal, an increase (decrease) in the first variable decreases (increases) the second variable below (above) what it otherwise would have been.”
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Polarity
• A →+ B Does not mean that if A rises
then B will rise over time
– Just says that B will be higher than it would
otherwise have been
– B may still be declining over time – but is
higher than it otherwise would have been
• A →- B Does not mean that if A rises then
B will decline over time
– Just says that B will be lower than it would
otherwise have been
– B may still be risingover time – but is higher
than it otherwise would have been
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Critical: Notion of “Increase”
• Must Clearly Distinguish
• Correct Interpretation: “if X were to INCREASE, would
Y increase or decrease compared to what it would have
otherwise been”?
• Different notion: “if X were to INCREASE, would Y
increase or decreaseover time”?
i.e. “if X were to INCREASE, would Y rise or fall over
time”?
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Causal Pathways • We can reason about the influence of one
variable and another variable by examining the
signs along their causal pathway
• Two negatives (whether adjacent or not) will act
to reverse each other
– Consider A →- B →- C
• An increase to A leads B to be less than it otherwise
would have been
• B being lower than it otherwise would have been causes
C to be higher than it otherwise would have been
• (compared to what it otherwise would have
been)
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Tips
• Variables will often be noun phrases
• Variables should be at least ordinal
• Links should have unambiguous polarity
• Indicate pronounced delays
• Avoid mega-diagrams
• Label loops
• Distinguish perceived and actual situation
• Incorporate targets of balancing loops
• Try to stick to planar graphs
• Diagrams describe causal not casual factors!
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Ambiguous Link
• Ambiguous Link: Sometimes +, sometimes -
• Replace this by disaggregating causal
pathways by showing multiple links
Rate of Weight
Gain
Basal Metabolism
Food intake Energy Surplus
Calories Burrt
Calories Taken in
+
++
+-
+
Rate of Weight
GainFood intake Energy Surplus
+
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Example 2
• Ambiguous Link: Sometimes +, sometimes
–
• Replace this by disaggregating causal
pathways by showing multiple links
Overtime
Fatigue
More Time
Working
Greater Incorporation of
Outside Tasks at Work
Efficiency+
+--
Work Accomplished
per Day
+
+
+
Overtime Work Accomplished
per Day+
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Example 3
• Ambiguous Link: Sometimes +, sometimes -
• Replace this by disaggregating causal
pathways by showing multiple links
Proportion of Fat
in Foods
Diet Caloric
Density
SatietyAmount of Food
Eaten
Calories Ingested+
+-
+
+
Proportion of Fat
in FoodsCalories Ingested
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Feedback Loops
• Loops in a causal loop diagram indicate
feedback in the system being represented
– Qualitatively speaking, this indicates that a
given change kicks off a set of changes that
cascade through other factors so as to either
amplify (“reinforce”) or push back against
(“damp”, “balance”) the original change
• Loop classification: product of signs in
loop (best to trace through conceptually)
– Balancing loop: Product of signs negative
– Reinforcing loop: Product of signs positive
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Example Vicious/Virtuous Cycles
• Positive (reinforcing) feedback can lead to
extremely rapid changes in situation Word of
Mouth Sales
Customers
+
+
+
# of Infectives
# New Infections
++
Prevalence of
Obesity
Prevalence of
GDM
Prevalence of
Macrosomic Infants
+
+
+
# of Activated
Memory Cells
# of Clonal
Expansions
++
Weight Perceived
as Normal
Individual Target
Weight
Mean Weight in
Population
+
+
+
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Example “Balancing Loops”
• Balancing loops tend to be self-regulating
MistakesLearning from
Mistakes
+
-
# New Infections
# of Susceptibles
-+
Hunger
Food Ingested
+-
Policy
Effectiveness
Policy
Reevaluation
Policy Adaptation
+
-
+
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Best Practice:
Incorporating Thresholds
• Balancing loops tend to be self-regulating
Hunger
Food Ingested
+-
Treshold for PolicyDissatisfaction to Lead to
ActionThreshold Hunger to
Motivate Eating
Policy
Effectiveness
Policy
Reevaluation
Policy Adaptation
+
-
+
Treshold for PolicyDissatisfaction to Lead to
ActionThreshold Hunger to
Motivate Eating
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Best Practice:
Indicating (Pronounced) Delays • Balancing loops tend to be self-regulating
Policy
Effectiveness
Policy
Reevaluation
Policy Adaptation
+
-
+
Treshold for PolicyDissatisfaction to Lead to
Action Hunger
Food Ingested
+-
Threshold Hunger to
Motivate Eating
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Elaborating Causal Loops
# of Infectives
# New Infections
+
+
# of Susceptibles
-+
Prevalence of
Obesity
Prevalence of
GDM
Prevalence of
Macrosomic Infants
+
+
+Study of Obesity
Creation of Nutrition
and Exercise Programs
+
+
-
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Classic Feedbacks
Infectives
New Infections
Susceptibles-
Contacts ofSusceptibles with
Infectives
+
+
+
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Broadening the Model Boundaries
Infectives
New Infections
People Presenting
for Treatment
Waiting Times
+
+
Health Care Staff
-
Susceptibles-
Contacts ofSusceptibles with
Infectives
++
++
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Example Vicious/Virtuous Cycles
• Positive (reinforcing) feedback can lead to
extremely rapid changes in situation
Existing Users
Likelihood of Cross Listingand Listing on Search
Engines
+
New Users
Discovering Site
+
Number of Connections to
Music Download Server
Length of Time Per
Download
Likelihood of User StartingMultiple Simultaneous
Downloads
+
+
+
Confusing Code
Ease of Understanding
where to Make a Change
Confusing
Additions
+
-
-
Word ofMouth Sales
Customers
+
+
+
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Elaborating Causal Loops
Number of Connections to
Music Download Server
Length of Time Per
Download
Likelihood of User StartingMultiple Simultaneous
Downloads
+
+
+
Users Abandoning
Download in Frustration
+
-
Number of Connections to
Music Download Server
Length of Time Per
Download
Likelihood of User StartingMultiple Simultaneous
Downloads
+
+
+
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More Elaborate Diagrams
Karanfil, 2008
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More Elaborate Diagrams 2
LaVallee& Osgood, 2008
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Causal Loop Structure :
Dynamic Implications
• Each loop in a causal loop diagram is
associated with qualitative dynamic
behavior
• Most Common Single-Loop Modes of
Dynamic Behavior
– Exponential growth
– Goal Seeking Adjustment
– Oscillation
• When composed, get novel behaviors due
to shifting loop dominance
– Behaviour of system more than sum of parts
– e.g. Growth and Plateau, “Boom and Bust”,
Lock-in
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CL Dynamics: Exponential Growth
(First Order Reinforcing Loop)
• Example
• Dynamic implications
Word ofMouth Sales
Customers
+
+
+
Graph for Stock
20,000
15,000
10,000
5,000
0
0 10 20 30 40 50 60 70 80 90 100
Time (Month)
Stock : Current
Site Popularity
Likelihood of Cross Listingand Listing on Search
Engines
+
+
From Tsai
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CL Dynamics: Goal Seeking
(Balancing Loop)
• Example:
• Dynamic behavior
PotentialCustomers
Word ofMouth Sales
-
+
-
Graph for Inventory
100
75
50
25
0
0 10 20 30 40 50 60 70 80 90 100
Time (Month)
Inventory : Current
From Tsai
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CL Dynamics: Oscillation
(Balancing Loop with Delay)
• Causal Structure
• Dynamic Behavior:
Inventory
FinishingProduction
ProducingStarts
DesiresInventory
-+
+
+
-
demand vs. product ion
6,857
3,142
0 30
Time (year)
demand : Oscil tons/year
producing : Oscil tons/year
From Tsai
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Growth and Plateau
• Loop structure:
– Reinforcing Loop
– Balancing Loop
• Dynamic Behavior:
Word ofMouth Sales
Customers
+
+
+
PotentialCustomers-
+
-
Graph for Customer
100,000
75,000
50,000
25,000
0
0 10 20 30 40 50 60 70 80 90 100
Time (Month)
Customer : Current
Existing Users
Likelihood of Cross Listingand Listing on Search
Engines
+
New Users
Discovering Site
+
Internet Users Yet to
Discover Site
-
+
From Tsai
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Complexities & Regularities
Department of Computer
Science
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Measles & Mumps in SK
Department of Computer
Science
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Example: STIs
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Three STIs: Test Volume vs Case
Counts
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TB Saskatchewan’s War on “White
Plague”
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Cases and Contact Tracing
0
1000
2000
3000
4000
5000
6000
1900 1920 1940 1960 1980 2000 2020
Contacts Examined
Incident Cases
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Contact Tracing Effort per Case
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Broadening the Model Boundaries: Endogenous Recovery Delay
Infectives
New Infections
People Presenting
for Treatment
Waiting Times
+
+
Health Care Staff
-
Susceptibles-
Contacts ofSusceptibles with
Infectives
++
++
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Common Phenomena In Complex Systems
• Counter-intuitive behaviour(Often fb interactions)
• Snowballing: When things go bad, they often go very
bad very quickly
– “Vicious cycles” lead to “cascading” of problems
(Due to positive feedback)
– “Path dependence”: Different starting points can
lead to divergence in project progress
(Due to positive feedback interacting w/ mult.
negative fb)
• Policy resistance: Situation can be unexpectedly
difficult to change
(Typically due to negative feedbacks that resist
change)
• Lock-in: Waiting raises barriers to improvement
(Due to positive feedback interacting w/ mult. negative
fb)
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Examples of Policy Resistance
– Cutting cigarette tar levels reduces cessation – Cutting cigarette nicotine levels leads to compensatory
smoking – Targeted anti-tobacco interventions lead to equally
targeted coupon programs by tobacco industry – Charging for supplies for diabetics as cost-cutting
measure leads to higher overall costs due to reduced self-management, faster disease progression, higher demand for dialysis & transplants
– ARVs prolong lives of HIV carriers, but lead to resurgent HIV epidemic due to lower risk perception
– “Saving money” by understaffing STI clinics, leads to long treatment wait, greater risk of transmission by infectives& bigger epidemics
– Antibiotic overuse worsens pathogen resistance – Antilock breaks lead to more risky driving – Natural feedback: Intergenerational “Vicious Cycles”
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Examples of Policy Resistance
– Cutting cigarette tar levels reduces cessation – Cutting cigarette nicotine levels leads to compensatory
smoking – Targeted anti-tobacco interventions lead to equally
targeted coupon programs by tobacco industry – Charging for supplies for diabetics as cost-cutting
measure leads to higher overall costs due to reduced self-management, faster disease progression, higher demand for dialysis & transplants
– ARVs prolong lives of HIV carriers, but lead to resurgent HIV epidemic due to lower risk perception
– “Saving money” by understaffing STI clinics, leads to long treatment wait, greater risk of transmission by infectives& bigger epidemics
– Antibiotic overuse worsens pathogen resistance – Antilock breaks lead to more risky driving – Natural feedback: Intergenerational “Vicious Cycles”
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Understanding Dynamic Complexity “Complexity is All Around Us”
Forrester JW. Counterintuitive behavior of social systems. Technology Review 1971;73(3):53-68.
Meadows DH. Leverage points: places to intervene in a system. Sustainability Institute, 1999.
Available at <http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf>.
Richardson GP. Feedback thought in social science and systems theory. Philadelphia, PA: University of Pennsylvania Press, 1991.
Sterman JD. Business dynamics: systems thinking and modeling for a complex world. Boston, MA: Irwin McGraw-Hill, 2000.
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Issues with Causal Loop
Diagrams • Unclear variables
• Diagrams can become very large
• Confusion regarding polarity
• Non-causal relationship
• Conservation not captured
• Behavior not always same as archetype
• Unclear paths/Missing causal factors
• Missing links
• Asymmetry in direction of change
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Unclear Variables
Variables Lacking Clear
Polarity
• Gender
• Ethnicity
• Shape
Often categorical & non-
ordinal
• Ask whether “more X” is
– Meaningful
– Unambiguous
Implicit Polarity
• Population (size)
• Revenue (amount of)
• Sound, Color (more of)
• Socioeconomic status
(more of)
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Unclear Links
• Causal loop diagrams should make clear
the causal pathway one has in mind
• One of the most common problems in
causal loop diagrams is showing a link
without the meaning being clear
– Often there are many possible pathways, and
distinguishing them can help make the
diagram much clearer
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Refining a Diagram
• It takes time to arrive at an acceptable
diagram
• Some of the biggest investments lie in
– Figuring out the appropriate variables to use
– Illustrating the different pathways
– Refining the names of the variables
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Very Large Diagrams
http://kim.foresight.gov.uk/Obesity/Obesity.html
Still useful for getting “big picture”
identifying where research “fits in”, research gaps
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Feedbacks Driving Infectious
Disease Dynamics
Susceptibles
New InfectionsContacts betweenSusceptibles and
Infectives
Infectives
+
++
-
+
New Recoveries
+-
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Example Dynamics of SIR Model (No Births
or Deaths)
SIR Example
2,000 people
600 people
10,000 people
1,500 people
450 people
9,500 people
1,000 people
300 people
9,000 people
500 people
150 people
8,500 people
0 people
0 people
8,000 people
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
Time (days)
Susceptible Population S : SIR example people
Infectious Population I : SIR example people
Recovered Population R : SIR example people
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Shifting Feedback Dominance
SIR Example
2,000 people
600 people
10,000 people
1,500 people
450 people
9,500 people
1,000 people
300 people
9,000 people
500 people
150 people
8,500 people
0 people
0 people
8,000 people
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
Time (days)
Susceptible Population S : SIR example people
Infectious Population I : SIR example people
Recovered Population R : SIR example people
Susceptibles
New InfectionsContacts betweenSusceptibles and
Infectives
Infectives
+
++
-
+
New Recoveries
+-
Susceptibles
New InfectionsContacts betweenSusceptibles and
Infectives
Infectives
+
++
-
+
New Recoveries
+-
Susceptibles
New InfectionsContacts betweenSusceptibles and
Infectives
Infectives
+
++
-
+
New Recoveries
+-
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Artifactual Loop
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Artifactual Loop 2
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Artifactual Loop 3
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State of the System: Stocks
(Levels, State Variables) • Stocks (Levels) represent accumulations
– These capture the “state of the system”
– Mathematically, we will call these “state
variables”
• These can be measured at one instant in
time
• Stocks are only changed by changes to the
flows into & out of them
– There are no inputs that immediately change
stocks
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Examples of Stocks
• Water in a tub or
reservoir
• People of different types
– { Susceptible,
infective, immune}
people
– Pregnant women
– Women between the
age of x and y
– High-risk individuals
• Healthcare workers
• Medicine in stocks
• Money in bank account
• CO2 in atmosphere
• Blood sugar
• Stored Energy
• Degree of belief in X
• Stockpiled vaccines
• Goods in a warehouse
• Beds in an emergency
room
• Owned vehicles
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Changes to State: Flows (“Fluxes”)
• These are always associated with rates
• If these flow out of or into a stock that
keeps track of things of type X, the rates
are measured in X/Unit Time (e.g.
person/year)
• Typically measure by accumulating people
over a period of time
– E.g. Incidence Rates is calculated by
accumulating people over a year
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Examples of Flows • Inflow or outflow of a
bathtub (litres/minute)
• Rate of infection (e.g.
people/month)
• Rate of recovery
• Rate of Mortality (e.g.
people/year)
• Rate of Births (e.g.
babies/year)
• Rate of treatment
(people/day)
• Rate of caloric
consumption
(kcal/day)
• Rate of pregnancies
(pregnancies/month)
• Reactivation Rate (#
of TB casess
reactivating per unit
time)
• Revenue ($/month)
• Spending rate
($/month)
• Power (Watts)
• Rate of energy
expenditure
• Vehicle sales
• Vaccines being
released
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Flows 2
• May be measured by totalling up over a period
of time and dividing by the time
• We can ask conceptually about the rate at any
given point – and may change over time
• When speaking about “Rates” for flows, we
always mean something measured as X/Unit
Time (also called a rate of change per time)
– Not all things called “rates” are flows
• Exchange rate
• Rate of return
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Key Component: Stock & Flow
StockFlow+
Stock
Flow
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Flow Impact on Stock
Stock
2,000
1,500
1,000
500
0
0 10 20 30 40 50 60 70 80 90 100
Time (Month)
Stock : Current
Flow
10
9.5
9
8.5
8
0 10 20 30 40 50 60 70 80 90 100
Time (Month)
Flow : Current
Stock
2,000
1,500
1,000
500
0
0 10 20 30 40 50 60 70 80 90 100
Time (Month)
Stock : Stock and Flow Alternative
Stock : Current
Impact of Lowering Flow (Rate) to 5/Month?
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Loops & Stocks
• Causation does not effect big change
instantaneously
– Loops are not instantaneous
• Stocks only change by changes to the flows
into & out of them
– There are no inputs that immediately change
stocks
• All causal loops must involve at least one
stock!
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Delayed Impact
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System Structure Diagrams
• Semi-quantitative models
• Combine causal loops diagram elements
with stock & flow structure
• Clearly distinguish stocks & flows
• If complete, all loops will go “through a
stock”
– Loop goes into the flow of a stock (as one
variable in the diagram)
– Loop comes comes out of stock (as next
variable in diagram)
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Headley et al., 2008
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Headley et al., 2008
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Disease
prevalence
Healthcare
assets
Insurance
coverage
Extent of
disease care
Complications
& Deaths
-
-
Risk
prevalence
Disease
incidence
Risk
management
-
Health protection
funding and
organizing -
Personal
healthcare
spending
Reimbursement and
coverage restrictions
-
Investment in
new assets -
Healthcare
prices
R1
B1
R2
B2
B3
B4
B5
Provider
adaptation
R3
Adverse behaviors
& living conditions
B6
(Disease management,
Urgent care)
System Structure Diagram
Homer, 2007