CROSS IMPACT ANALYSIS

Lekshmi Krishna M.R100609

Department of Future StudiesUniversity of Kerala

CONTENTS

• Introduction• Cross impact Analysis (CIA)

History of CIA Objective of CIAPhases of CIAProcedure of CIA Description of methodSensitivity testing and Policy testingStrengths and Weakness

• Reference

Introduction

• Developed by Theodore Gordon and Olaf Helmer in 1966

• The method was based on a simple question

Can forecasting be based on perceptions about how future events may interact ????????

Objective of CIA

• Scenario development to visualize the possible future of subject

• No of possible scenarios = 2^n

n = No of events

Phases of CIA

• Early exploratory phase

• Probabilistic phase

• Synthesis phase

• Application phase

Procedure of CIA 1. Select a team of experts in the subject of interest

2. The team of experts will identify the most relevant events

3. The team of experts will then assess their best guess about the probability of each event

4. Then the team of experts will construct the cross-impact matrix

5. On the basis of the information of the cross-impact matrix, the team of experts will have to assess the initial conditioned probabilities

6. After assessing the initial probabilities, simulate the process of event-occurrence using the Monte Carlo technique

7. Establish the new values for all initial probabilities

8. Repeat the simulation process taken as input the new refined or reviewed probabilities

9. From the results of the latest simulation exercise the team of experts will obtain the probability of occurrence of each possible scenario.

IMPACT MODELS

DIRECT IMPACT

A

B C

A

B

D

C

INDIRECT IMPACT

MATRIX METHOD

• Find the set of variables

• Initial probability

• Conditional probability

• Impact of matrix (odd ratios)

• Initial probability

___ ___

P(1) = P(2).P(1/2) + P(2).P(1/2)

___ ____

P(1/2)= P(1) – P(2).P(1/2)

------------------------

P(2)

Conditional probability

Max P(1/2) = P(1) / P(2)

Min P(1/2) = P(1) – P(2) --------------- P(2)

Max P(1/2) CP Min P(1/2)

Suppose the initial probability and conditional probability are defined

as belowEvents Initial

probability

1 2 3 4 5

1 0.25 0.50 0.85 0.40 0.35

2 0.40 0.60 0.60 0.55 0.50

3 0.75 0.15 0.50 0.60 0.25

4 0.50 0.25 0.70 0.55 0.15

5 0.30 0.70 0.80 0.65 0.35

Odd matrix calculationprobability/(1-probability)

Initial probability

1 2 3 4 5

1 0.33 1.00 5.67 .67 0.54

2 0.67 1.50 1.50 1.22 1.00

3 3.00 0.02 1.00 1.22 0.33

4 1.00 .33 2.33 1.22 0.18

5 0.43 .33 4.00 1.86 .54

Odd matrix ratio calculationDivide the column matrix with corresponding row

Eg :- P(variables in column 1/Initial probability of 1)

Events Initial probability

1 2 3 4 5

1 0.33 1.50 1.90 0.67 1.26

2 0.67 4.50 0.50 1.22 2.33

3 3.00 0.07 1.50 1.22 0.77

4 1.00 1.00 3.50 0.41 0.42

5 0.43 1.00 5.97 0.62 0.54

MONTE CARLO TECHNIQUE

• Class of computational algorithms rely on repeated random sampling

• Occurrence and Non Occurrence of Events

• TreeAge pro

• SMIC : Statistically valid possible scenarios

Evaluation

• Choose a random variable say .75

• Check the variables and find the relationship

• Generate tables by computations

• Generate different scenarios

Analysis

• By using the different matrix obtained

Sensitivity Testing

• Select a particular judgment

• Change that judgment and run matrix again

• Significant difference : The judgment is important

• No significant difference : The judgment is

relatively unimportant

Policy Testing

• Define an anticipated policy that affect the events in the matrix

• The matrix changed wrt to policy• Run the matrix• Compare with the calibrated run• Difference due to policy• Changes can be traced back through the matrix• Effect of policy can be determined

Graph method

• Find the set of variables

• Define the matrix

• Take row and column sum

• Row sum = Influential

Column sum = Dependent

• Plot graph X axis =Dependency

Y axis = Influential

Var 1 Var 2 Var 3 Var j Influence

Y coordinate

Var 1 0 Var 2,1 Var 3,1 Var j,1 Var 2,1+Var 3,1+Var j,1

Var 2 Var 1,2 0 Var 3,2 Var j,2 Var 1,2+Var 3,2+Var j,2

Var 3 Var 1,3 Var 2,3 0 Var j,3 Var 1,3+Var 2,3+Var j,3

Var i Var 1,i Var 2,i Var 3,i 0 Var 1,i+Var 2,i+Var 3,i

Dependence

X coordinate

Var 1,2+Var 1,3+Var 1,i

Var 2,1+Var 2,3+Var 2,i

Var 3,1+Var 3,2+Var 3,i

Var j,1+Var j,2+Var j,3

Impact activity scheme Adapted from Scholz and Tietje (2002)

Influential Variables Ambivalent Variables

Buffer Variables Dependent Variables

Analysis

• 1st quadrant : Highly influential and dependent variables

• 2nd quadrant : Highly influential variables

• 3rd quadrant : Less influential and dependent variables

• 4th quadrant : Highly dependent variables

Procedure for using graph matrix

Event Initial probability

1 2 3 4 5 Influence

1 0.25 0.50 0.85 0.40 0.35 2.10

2 0.40 0.60 0.60 0.55 0.50 2.25

3 0.75 0.15 0.50 0.60 0.25 1.50

4 0.50 0.25 0.70 0.55 0.15 1.65

5 0.30 0.70 0.80 0.65 0.35 2.50

Dependency

1.70 2.50 2.65 1.9 1.25

Probability distribution due to a positive impact

Benefits

• Limited skills required

• Forces attention of the respondents

• Estimates dependency and interdependency between issues

Weakness

• Collection of data is tedious

• Probability may not be accurate

• In real world interaction not only involve pairs but also events of higher orders

ConclusionIn recent years, the work on cross-impact has shifted from "pure" methodological development to applications.

Questions about the method remain, of course: how best to ask questions about conditional probabilities; is the method really convergent; how to handle non-coherent input from experts; how to integrate with other methods?

But there is no doubt that cross impact questions helps to illuminate perceptions about hidden causalities and feedback loops in pathways to the future.

.

~~~Thank you~~~

Reference

• Cross Impact Analysis : Theodore Jay Gordon• Cross impact balances : A system theoretical approach to CIA by

Wolf gang• Seminar on Future Research methodologies for the United States• Introduction to qualitative systems and scenario analysis using

Cross Impact Balance Analysis : W. Weimer Jehle• Brief over view of some Futures Research Methods : Jerome C

Glenn• Critical look at the cross impact matrix method : Michael Folk• An elementary cross impact model : Norman C Dalkey • A new look at the Cross Impact Matrix and its application in Future

Studies : Kenneth Chao • http://foresight.jrc.ec.europa.eu/documents/eur17311en.pdf