The Cross Study of Nonlinear Modeling Methods

The Cross Study of Nonlinear Modeling Methods

Hans J. (Jochen) Scholl

University at Albany / SUNY

MIT Field Trip, 4/20//2001 Hans J. (Jochen) Scholl Slide 2

What has this topic to do with What has this topic to do with Information Science?Information Science?

Why has it NOT to do with Information Science? The understanding of Information Science rests on the understanding

and definition of “information”– Shannon’s engineering perspective (physical transmission)

– Context / meaning of “information”

– Buckland (“process” - “thing” - “knowledge”)

– Quigley and Debons (just text answering to “NEOT” versus “WY”)

– Buckland (“observation of phenomena that have the capacity to be informative”)

– Norton (“fundamental link among all what we are, know, and do not know”)


What has this topic to do with What has this topic to do with Information Science? Information Science? (more)(more)

Lipetz ( “facilitation of utilization of records”) Georgia Institute of Technology (1961)

– “The science that investigates the properties and behaviors of information, the forces governing the flow of information, and the means of processing information for optimum accessibility and usability. The processes include the origination, interpretation, and use of information. The field is derive from or related to mathematics, logic, linguistics, psychology, computer technology, operations research, the graphic arts, communications, library science, and some other fields” (Shera & Cleveland)

Paisley (“IS is not retrievology”) Borko’s list of nine application fields (…(6) system design, (7) analysis and

evaluation, (8) pattern recognition, (9) adaptive (and self-organizing) systems) Otten and Debons (“Metascience - framework for all information-oriented

sciences”) Skovira (“Pluralism in understanding of IS”)


The Information Science ContinuumThe Information Science Continuum

MetascienceParent Disciplines

MathematicsComputer ScienceLinguisticsORPublic AdministrationPsychologyBusiness Administration….Library Science

An Information Scientist is trained inand has a natural interest in crossstudies and multi-method approaches


Research Methods and ToolsResearch Methods and Tools It is all about models Traditional Research

– Mathematical or linguistic models : rigorous versus flexible– Quantitative / qualitative – Underlying principle: "(1) the cause precedes the effect in time, (2) there is an empirical

correlation between them, and (3) the relationship is not found to be the result of some third variable” (Babbie,

1999) – Best applied to relatively simple, linear systems and when coping

with relatively narrow / limited data spaces Computer-based experiments

– Vast data spaces– Flexible AND– Rigorous


The Notion of Comparative ResearchThe Notion of Comparative Research

Problem pi with i=1,…n and piPMethodology mj with j=1,…m and mjM Result rk with k=1,…r and rk R

What rR found through mM when applied to explain a certain pP• correspond / are similar / are equal?• differ / contradict?• neither correspond nor contradict / complement ?

What rR can be expected when combining certain mM to explain / triangulate a certain pP?


The More Specific Research QuestionThe More Specific Research Question

What dynamic problems have been explained by means of which methodology?

What where the findings in cases when more than one methodology was applied to a dynamic problem?

What are the insights from comparing the findings? What are strengths and limitations of the methodologies used when

applied to explain the dynamic problem at hand? What are potential benefits of multi-method research designs? Case in point: The Beer Distribution Game


Usage of TermsUsage of Terms Linearity

– A relationship is linear if the effect on a dependent variable of a change of one unit in an independent variable is the same for all possible such changes

Nonlinearity (ergo)– A relationship is nonlinear if the effect on a dependent variable of a change

of one unit in an independent variable is NOT the same for all possible such changes

Nonlinearity – If f is a nonlinear function or an operator, and x is a system input (either a function or

variable), then the effect of adding two inputs, x1 and x2, first and then operating on their sum is, in general, not equivalent to operating on two inputs separately and then adding the outputs together; i.e. . Popular form: the whole is not necessarily equal to the sum of its parts. Dissipative nonlinear dynamic systems are capable of exhibiting self-organization and chaos. (Nonlinear Dynamics and Complex Systems Theory, Glossary of Terms - http://www.cna.org/isaac/Glossb.htm#Nonlinearity - access date 04/09/2001)


Usage of Terms Usage of Terms (more)(more)

Nonlinearity– “a system is nonlinear if it contains a multiplication or division of variables or if it

has a coefficient which is a function of a variable (Forrester, 1968)

“Degree of (a system’s) nonlinearity – implies the number of policies in the system that are nonlinear (ibid.)

Complexity in systems– multiple interconnected positive and negative feedback loops containing

nonlinearity (ibid.)

Complex systems – have seven characteristics: (1) counterintuitive, (2) insensitive to many parameter

changes, (3) resistant to policy changes, (4) pressure or leverage points, (5) compensate for externally applied pressure, (6) short-term behavior may differ from long-term behavior (7) tendency to low performance (social systems) (Forrester, Urban Dynamics, 1969)



Emergence – “… a product of coupled, context-dependent interactions (which) , and the

resulting system, are nonlinear “ (Holland, Emergence, 1999) Nonlinearity

– “The behavior of the overall system cannot be obtained by summing the behaviors of its constituent parts” (ibid.)

Complexity– (generated) emergent system behavior based on simple laws



Stanislaw Ulam reportedly said (something like) "Calling a science 'nonlinear' is like calling zoology 'the study of non-human animals’ (J.D. Meiss, sci.nonlinear FAQ )

Nonlinearity – In geometry, linearity refers to Euclidean objects: lines, planes, (flat) three-

dimensional space, etc.--these objects appear the same no matter how we examine them. A nonlinear object, a sphere for example, looks different on different scales--when looked at closely enough it looks like a plane, and from a far enough distance it looks like a point.

– In algebra, we define linearity in terms of functions that have the property f(x+y) = f(x)+f(y) and f(ax) = af(x). Nonlinear is defined as the negation of linear. This means that the result f may be out of proportion to the input x or y. The result may be more than linear, as when a diode begins to pass current; or less than linear, as when finite resources limit Malthusian population growth. Thus the fundamental simplifying tools of linear analysis are no longer available (ibid)



Complex Systems

– are spatially and/or temporally extended nonlinear systems characterized by collective properties associated with the system as a whole--and that are different from the characteristic behaviors of the constituent parts.

– While, chaos is the study of how simple systems can generate complicated behavior, complexity is the study of how complicated systems can generate simple behavior. An example of complexity is the synchronization of biological systems ranging from fireflies to neurons.

– In these problems, many individual systems conspire to produce a single collective rhythm. (ibid.)


Agent-based Modeling (ABM)Agent-based Modeling (ABM) Individual or agent as

unit of analysis Behavior governed by

(few) rules Global consequences of

individual interaction Complex, nonlinear

behavior Emergence

Boids’ Three Rules (Craig Reynolds)

1. Maintain a minimum distance from other objects in the environment, including other boids.

2. Match velocities with boids in its neighborhood.

3. Move toward the perceived center of mass of boids in its neighborhood.


System Dynamics Modeling System Dynamics Modeling (SDM)(SDM)

Causal relationships between system elements

Stocks and flows Feedback loop as unit of

analysis Positive (that is, reinforcing

feedback) and Negative (that is,

counterbalancing or goal-seeking feedback)

Differential equations Pattern of complex / nonlinear

behavior rooted in system structure - endogenous behavior

initial x

X

S

Y

RminusZR

Z

B

dX dt

dZ dt

dY dt

Graph for Y

40

0

-40

0 10 20 30 40 50Time (time)

Y : base28001Y : base27999Y : base28

Deterministic chaos: Lorenz’s weather equations


Characteristics & Fields of StudyCharacteristics & Fields of Study Overlapping fields of study

– Economics, ecology, biology, anthropology, psychology, sociology, economics, traffic simulations, military, model testing

– Tragedy of the commons,deer management, predator/prey, beer game ABM

– Inductive / generative– Individual / rule based– Emergent system behavior– More than one unique set of agents/rules could lead to similar emergent behavior– Path from emergent behavior down to agent/rule level can be difficult

SDM– Deductive / analytical – Aggregate– Leverage / intervention points– Causal relationships debatable - expert consensus


Similarities and DifferencesSimilarities and Differences According to Phelan, almost identical meaning and usage of terms

such as system, emergence, dynamic, nonlinear, adaptive and hierarchy.

Both theories also share a belief that there are universal principles underlying the behavior of all systems.

“Confirmatory analysis” and “problem solving perspective”, “generating shared understanding and consensus one requires to improve the system” (SDM) as opposed to mainly exploratory research (ABM).

Individual versus aggregate


Epistemological AspectsEpistemological Aspects ABM modelers typically take positivist to extreme positivist positions SDM modelers range from positivist to constructivist positions However, as seen earlier, positivist positions suffered from a serious

attack from within (deterministic chaos)


A Remarkable BeginningA Remarkable Beginning John H. Miller’s ANTs (Active, nonlinear tests)

– A simulation model is subjected to automated testing by use of hill-climbing and genetic algorithms (mutation and crossover). Vast test spaces result

– Sensitivity of a model’s variables to parameter changes in very wide test spaces (zillions of solutions) is uncovered which leads to a better assessment of model validity

– World3 as case in point


The Bullwhip EffectThe Bullwhip Effect SD treatment

– Forrester, Industrial Dynamics (1958)• Multi-echelon supply chain are “by virtue of policies, organization, and

delays…naturally oscillatory”

• Remedies – Faster order handling

– Better information along the chain regarding consumer demand

– Modest and gradual inventory adjustments

– Sterman, Misperceptions of Feedback (1989a & b)• Beer distribution game experiment

• Simulation of an economy

– Peter Senge, The Fifth Discipline (1990)• No strategy - pass on order rule


The Bullwhip Effect The Bullwhip Effect (more)(more)

Economics / Traditional Management Science Treatment– Lee et al, (1997)

• Distorted information as cause and “rational decision-making”

– Demand signaling

– Order batching

– Price fluctuations

– Rationing and shortage gaming

• Recommended remedies: (1) information sharing, (2) channel alignment, (3) improved operational efficiency

• Strategic interaction among rational supply chain members



Agent-based Modeling Treatment– Kimbrough et al, (2001)

• ABM implementation of the MIT (stationary input) and the Columbia (stochastic inputs) beer games

• AlgorithmInitialization. A certain number of rules are randomly generated to form generation 0.

2) Pick the first rule from the current generation.

3) Agents play the beer game according to their current rules.

4) Repeat step 3, until the game period (say 35 weeks) is finished.

5) Calculate the total average cost for the whole team and assign fitness value to the current rule.

6) Pick the next rule from the current generation and repeat step 2, 3, and 4 until the performance of all the rules in the current generation have been evaluated.

7) Use genetic algorithms to generate a new generation of rules and repeat steps 2 to 6 until the maximum number of generations is reached

• Experiments– Mimicking the MIT game -> pass-order rule found - Nash equilibrium

– Stochastic demand input -> agents find better rules than pass-order - no bullwhip effect

– Stochastic demand and stochastic lead time -> agents stiff find better rules and again - no bullwhip effect



Areas of Agreement and Departure– Traditional research claims the rationality of (local) decision-making

• March & Simon (1958) discussed the demands of such a proposition: (1) all alternatives of choice are given; (2) all consequences are known under certainty, risk, and uncertainty; (3) rational man has complete utility-ordering

• Lee’s et al definition of rationality is not specified

• Evidence for the lack of local rationality mounting (Sterman, Moxnes)

– No disagreement on other areas (demand inflation, amplification, etc.)

– ABM literature is silent about the causes of the bullwhip effect

– All three strands agree on the remedies (except changing the mental models as proposed by SD)

– ABM demonstrates the existence of better than pass-order solutions

– ABM also confirms the “perceptional source” of the bullwhip effect


ConclusionConclusion Certain similarities despite differences in basic concepts and

understandings Dynamic modeling techniques may have a capacity to complement

each other (as in the case of the beer game) Study of findings and research designs Understanding strengths and limitations of each modeling technique Potential for triangulation “Basic problem” cross study will continue

– Predator/prey– Deer management– Tragedy of the commons

Integrated research designs


The Hawaiian International Conference on The Hawaiian International Conference on System Sciences (HICSS)System Sciences (HICSS)

According to MIS Quarterly (1997) the second most important conference in its field (after ICIS, and before IFIP, DSS, …, Cad.of Mgmt etc.)

This year over 650 attendees (40 percent of whom came from overseas) 85 percent of attendees present papers Nine main tracks, dozens of minitracks The 35th conference will be held next January, 7-10


HICSSHICSS

Very productive– Over fifty percent of presented papers become journal articles of

monographs Tracks of Special Interest

– Complex Systems

– Decision Technologies for Management


Decision Technologies for Management Decision Technologies for Management TrackTrack

Minitrack “Modeling Nonlinear Human and Natural Systems” (formerly Agent-based Modeling and System Dynamics) - the minitrack invites papers– From an SD perspective

– From an Agent-based modeling perspective

– From other nonlinear modeling disciplines

– Highly welcome are papers which incorporate various modeling techniques

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The Cross Study of Nonlinear Modeling Methods

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