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Causal Modeling & Simulation�Profs. Aseem Kaul & Andy Van de Ven�MGMT 8104, Research Design, Session 3�

Plan for Class

Introduction & Questions on Readings & Video on Modeling

Harrison et al, Simulation modeling , AMR 2007
Knudsen et al, A model is a model, Strategy Science, 2019
Puranam, et al, Modeling bounded rationality, AMA, 2015
Dooley, Conceptualizaing Org change through lens of complexity science, 2021
Example: Chen, Kaul & Wu, Adaptation across multiple landscapes, SMJ 2019
Example: Dooley, Conceptualizing … Complexity Science, Handbook 2021.

Causal modeling exercise
Presentation & discussion of a few modeling designs

Chapter 5 of Engaged Scholarship introduces two basic types of research questions:

What are the antecedents or consequences of a phenomenon?

How does the phenomenon emerge, develop, grow or terminate over time?

These what and how questions represent a “fork in the road” for designing research.

What questions entail a variance model, or outcome-driven explanation of the input factors (independent variables) that explain variations in some outcome criteria (dependent variables).

How questions require a process model or event-driven explanation of the temporal order and sequence in which a set of events occur based on a story or narrative.

Three basic suggestions:

Understand your research question, and select the model appropriate for examining your research question.
Understand the assumptions, strengths & limitations of variance and process models you construct to examine your research question.
Assess variance and process models on their own terms; not in terms of the other.

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Discussion of Causal Modeling Readings/Video�

Chris Winchester	Formal modeling is very new to me, so my main struggle is wrapping my head around the process of developing a formal model. Can you provide an example of a formal model and how you went about developing this from the initial thought/RQ to the final (or most recent) version? I think this would be very helpful for me and others to see an example of model development "in action".
Hanu	Is there a structure/guide to contrast the kind of problems that lend themselves naturally to models from those that do not? For example, a naive way would be to use models when data is hard to get
Chelsea Garcia	The concept of "low hanging fruit" came up in the video and I am curious if there is still low hanging fruit to be uncovered in the HRD world? I haven't come across a lot of process model studies in the research.
Bo Fang	It seems to me that we could use formal modeling to answer both "how" and "what" questions, but I wonder whether it belongs to the variance model or the process model, or is it a unique approach that we can consider using for any type of research problem/question?
Jooyoun	1. How could one critically review modeling papers? Are there things different from what we are trained to pay attention to when reviewing theory or empirical papers?�2. You've written out modeling papers with different approaches from a pure modeling paper to a hybrid of modeling and hypotheses testing. What led you to take different approaches?
Justine Mishek	The idea of stacking simulations - or a building block approach - is also noted in the Harrison reading, particularly when seeking to uncover practical insights and use. (p1241, 2nd paragraph) Harrison also suggests that simulations should keep it simple. Overall, is simple viewed as 'elegant' or is simple considered 'less than' in academic circles? Is simplicity really the desired state in simulation circles? If not, could this lead to what Knudsen refers to as a 'cave of fellow modelers' and reduce the impact models /simulations can have in practice?
Yeonjoo Lee	How do you choose between modeling, empirical data, and mixed-method paper when you're designing a study? Do you recommend conducting a mixed-method study when it's possible?

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Why build a model?

Clarity

Precise definition of constructs
Transparent assumptions

Rigor

Logical validity
Equilibrium with multiple actors

Insight

Deeper understanding of mechanisms
Complex relationships (e.g., n-way interactions)
Non-intuitive findings
Clear derivation of boundary conditions

These benefits derive from (and come at the cost of) substantial simplification of the real world

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Choosing a model

Analytical models

Clear understanding of underlying mechanisms
Full range of potential parameter values
Rigorous derivation of thresholds / cut-off points

Simulations

Multiple / heterogeneous actors
Uncertain or stochastic processes (role of chance)
Greater distance from starting assumptions
Observe change process

Often useful to start from a pre-existing model and make changes to the set-up or relax prior assumptions, rather than starting from scratch

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Designing a Formal Model (example 1)

Luo, Kaul, & Seo, SMJ (2018), ‘Winning us with trifles’

Q1. Model type: Analytical (variant of Rothschild & Stiglitz, 1976)

Q2. Key tension: Moral Hazard (philanthropy offers protection in case of accidents, but both philanthropy and accidents are firm choices)

Q3. Agents: Firms (2 types: clean & dirty); Society

Q4. Decision rules: Firms maximize profits; Society minimizes (or satisfices) accident frequency

Q5. Key Assumptions: Only the firm knows its type; firm can (partially) control accident probability

Q6. Parameters to vary: Society active vs. passive, Firms profit-maximizing vs. altruistic

Q7. Outcome measures: Corporate donations, Accident probability

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Designing a Formal Model (example 2)

Chen, Kaul, and Wu, SMJ (2019), ‘Adaptation across multiple landscapes’

Q1. Model type: Simulation; variant of NK model (Levinthal, 1997)

Q2. Key tension: Sharing resources across businesses produces synergies, but also limits the firm’s ability to adapt

Q3. Agents: Diversified firm vs. 2 focused (single business) firms

Q4. Decision rules: Firms search locally; diversified firm maintains consistency across related decisions

Q5. Key Assumptions: Synergies between related businesses require coordination; diversified firm will always coordinate related elements (relaxed in supplementary analysis)

Q6. Parameters to vary: Relatedness between business, complexity within businesses, level of synergy

Q7. Outcome measures: Long-term diversification advantage

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Exercise in Designing a Formal Model

Q1. What type of model would you choose?

Q2. What is the key tension / tradeoff you are trying to model?

Q3. Who are the agents in the model? how many of them are there and are they of different types?

Q4. What are decision rules each agent will follow?

Q5. What are the key assumptions that you will hold constant throughout the model?

Q6. What are the (1 or 2) key parameters you plan to vary?

Q7. What are the outcomes measures you want to track?

Breakout exercise: Discuss questions in pairs and then come back and share a few examples

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Designing Simulation Modeling Studies

Harrison, Lin, Carroll & Carley, 2007. Simulation modeling in organizational and management research, AMR.

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Kauffman’s NK(C) Model of Complexity

NK(C) Systems

– N = # of Elements (Boolean Nodes) in the system

– K = degree of interdependence among elements (# of connections that a node accepts as inputs)

– C = degree of the system’s coupling with other coevolving systems in the landscape (# of connections each node has to nodes of another system)

Kauffman introduced an interesting model based on Boolean networks. The network consists of nodes that turn on and off depending on the state of other nodes to which they are connected

N is the number of elements in the system

K is the degree of interdependence among elements in the system, which are number of connections that a node accepts as inputs

C is the number of connections each node has to nodes of another system, meaning the system’s coupling with other system in the landscape

NK model emphasizes the importance of self-organization and local action in producing system outcomes( in contrast to traditional theories of central design and control) The interaction of elements in a system can produce surprising, emergent behavior that can be modeled in terms of ﬁtness landscapes.

The ﬁtness landscape, a concept originally developed in evolutionary biology by Sewell Wright , has been formalized by Kaufmann (1993) and applied to studies of organizational adaptation by many other scholars such as Levinthal (1997), McKelvey (1997), Siggelkow (2001), and Rivkin (2000), among others.

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Single vs. Rugged Landscape

Low K (Degree of interdependence)

Single peaked landscape

Rugged landscape

High K (Degree of interdependence)

Levinthal and Warglien (1999, pp. 344–345) employ the NK model and bring new perspectives of fitness landscapes.

They examined alternative kinds of ﬁtness landscapes that emerge with variations in K and N . When K is low compared to N, in other words, there is low degree of interdependence among components, the landscape will tend to have a very large smooth basin with a single peak which means there is one best approach for optimal output. So in this situation, components or actors can pursue universal best practices without having to consider relationships with other components.

Therefore, behavior of autonomous actors is highly predictable without having to know their speciﬁc choices or starting points on the landscape. On this single peaked landscape best configuration of work modules (internal fit) is to minimize interdependence among components. Levinthal and Warglien point out that a single-peak ﬁtness landscape “solves the problem of coordination, but it does so at the cost of diversity” (1999, p. 347)

In contrast, when K is high, the landscape shape into a rugged landscape with multiple peaks, which means there is not a single optimum solution. Thus This situation encourages searching for various and equifinal (equally effective) alternative conﬁgurations. A problem here is it increases the unpredictability in collective behavior. A change by any component inﬂuences other components in the system, often in dysfunctional ways (i.e., reducing performance),.This is a dynamic representation of the conﬁguration perspective where changing a single component in a system may diminish effectiveness if they do not change other core interdependent components. As Levinthal and Warglien state, “Search in rugged landscapes is basically the search for new sets of complementarities” (1999, p. 348).

-> soccer configuration example (3-4-3) (4-4-3) (1-3-4-2)

Moving from one design conﬁguration to another configuration (from a hill to another hill) typically entails some random exploration, and the risks of forgoing the beneﬁts of known, attractive sets of behavior. Instead of moving hill to hill, if you just want to make incremental changes in a design conﬁguration represents suboptimal movements up or down a local hill. Shifting between hills is necessary when “breakthrough” and “platform” innovations are desired.

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Work Design Performance Landscapes�Internal and External Fit of Mass (Ford) and Lean (Japanese) �Automobile Production Systems in Early 1900s and in 1980s

The Ford production system in early 1900s

Rise of Japanese Production System in 1980s and relative decrease of the Ford system

Source. Siggelkow (2001, p. 840)

Siggelkow (2001) illustrates how notions of internal and external ﬁt can be translated to ﬁtness landscapes. He graphs the performance landscape of the Ford Motor Company’s low- variety/low-ﬂexibility mass production system in the early 1900s (Figure 2a) and illustrates how its performance decreased in comparison with the Japanese (Toyota) high-variety/high-ﬂexibility lean production system in the 1980s (Figure 2b).

Internal ﬁt (i.e., the internal coherence of a particular design conﬁguration) is represented by a peak in the land- scape, and the steepness of the peak is a function of the interdependencies among components of the con- ﬁguration: “Internal ﬁt corresponds to a peak because changing any single element (and not changing any other element) within a consistent set of choices leads to a decline in performance” (Siggelkow 2001, p. 840)

Environmental changes during the 1900s are represented by changes in the height, shape, and location of existing peaks and the emergence of new peaks on the ﬁtness and scapes in Figures 2a and 2b.

For instance, given the production technologies available in the early 1900s, low-variety/low-ﬂexibility production systems were very efﬁcient. However, the performance of this work system conﬁguration declined relative to the high-variety/high- ﬂexibility production conﬁguration that became techno- logically feasible by the 1980s.behavior.

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Empirical Modeling of Time Series Data

Problem:

We have time series data on innovation development events.
We do not know their temporal pattern.
What kind of equations model the data?

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Four Types of Empirical Time Series

Type of time series	Dimensionality (# of causal factors)	Type of Interaction between variables	Appropriate model
Periodic	Low (2-3 dimensions)	Independent or linear	linear deterministic models (regression analysis)
Chaotic	Low (5-9 dimensions)	Interdependent in a non linear fashion	NK(C) model * Fitness landscape
Colored (pink) noise (generated according to power laws)	High (many dimensions)	Interdependent in a non linear fashion	NK(C) model * Fitness landscape
White noise (Truly random dynamic)	High (many dimension)	Independent or linear	Probability models

Adopted from Anderson et al. (1999) and Sinha and Van de Ven (2005). Designing work within and between organizations. Organization Science, 16(4), 389–408p.

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Dynamical Landscape

Few variables acting

independently

Many variables acting

independently

Many variables acting

interdependently

Few variables acting

interdependently

Statistical

Analysis

CHAOS

PERIODIC

WHITE

NOISE

COLORED

NOISE

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Self-Organizing Criticality:� CIP Actions in Beginning Period

log-normal: distributional fractal

Kevin Dooley

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Diagnostic Tests for Chaotic and �Non-Linear Patterns in Time Series

Lyapunov Exponent
Correlation Dimension
BDS Statistic
Periodic ARIMA modeling
Granger Causality
Power Laws

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Example of Modeling Complexity

Let us model the relative time spent on exploration versus exploitation activities over time in an organization with the following logistic map:

X_t = kX_t-1(1-X_t-1)

Where:

X_t = if actions taken at time t are exploration

vs. exploitation activities

k = parameter governing the degree of non-linearity of the� equation

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k = 1.8

k = 3.2

k = 3.7

When k in

X_t= kX_t-1(1-X_t-1)

Equals:

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Bifurcation Structure of the Limit Set of Logistic Map X_t = kX_t-1 (1 – X_t-1) for varying values of k

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Lorenz and Mandelbrot Attractors

Edward Lorenz Benoit Mandelbrot

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A Chaotic Process is Dynamic, Non-Linear and Sensitive to Initial Conditions

Dynamic means that the values a variable takes on at any time t are a function (at least in part) of the values of that variable at an earlier time, e.g. path dependence.

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A Chaotic Process is Dynamic, Non-Linear and Sensitive to Initial Conditions

Non-linearity implies that dynamic feedback loops vary in strength (loose or tight coupling) and direction (positive or negative) over time.

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A Chaotic Process is Dynamic, Non-Linear and Sensitive to Initial Conditions

Small initial differences or fluctuations in variables may grow over time into large differences, and as they move further from equilibrium, they bifurcate or branch out into numerous possible pathways.

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Problem

We have time series data on innovation development events.
We do not know their temporal pattern.
What kind of equations model the data?�
Case Example: Cochlear Implants

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Next Class: Designing Process Research Models�

Plan for Class

Discuss readings & video lectures
Issues in designing process research models
Student breakouts on process research worksheets

Key Point:

Process research should be evaluated on its own terms;

not in terms of variance research models.

Chapter 5 of Engaged Scholarship introduces two basic types of research questions:

What are the antecedents or consequences of a phenomenon?

How does the phenomenon emerge, develop, grow or terminate over time?

These what and how questions represent a “fork in the road” for designing research.

What questions entail a variance model, or outcome-driven explanation of the input factors (independent variables) that explain variations in some outcome criteria (dependent variables).

How questions require a process model or event-driven explanation of the temporal order and sequence in which a set of events occur based on a story or narrative.

Three basic suggestions:

Understand your research question, and select the model appropriate for examining your research question.
Understand the assumptions, strengths & limitations of variance and process models you construct to examine your research question.
Assess variance and process models on their own terms; not in terms of the other.

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Exercise: Students share & assess their process study designs

Issues	Your Process Research Study
1. State your process research question Whose viewpoint is featured?	Process models are geared to studying how questions
2. State your key process proposition. What process theories do you examine?	Apply and compare plausible alternative models
3. How define process ? What is your unit of analysis?	As an assumption, variable or event? Unit of time?
4 What is your process research design?	- concepts/units examined over time - real-time or historical event data - archival, laboratory, or field study
5. How measure process concepts?	- What is an incident/event? - How measure & verify it? - How tabulate and organize data?
6. How sample cases & events?	- sample diversity in what dimensions? - Sample size - # of events vs. cases
7. How analyze data to develop or test your process proposition?	Match data analysis methods To number of cases and events
8. What are the threats to study validity?	- process pattern observed? - replicable methods? - reliable measurements? - story verisimilitude?

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EXTRA SLIDES IF QUESTIONS ARISE�

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(Source: Hibbert & Wilkinson, 1994, pp. 218)

Lyanupov Exponent

Tests for sensitivity to initial conditions

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Correlation Dimension

Measures the way points of a time series are scattered in d-dimensional space

If random, the points scatter to fill d-dimensional space
If chaotic, the points cluster in bounded low-dimensional space

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Brock, Dechert & Scheinkman�(BDS) Statistic

Tests for independent and identically distributed observations to determine if a time series is non-linear

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Different Colors of Random Processes

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Self-Organized Criticality

“self-organized criticality” is one route to dynamical fractals (pink noise)

pattern of critical thresholds, punctuated equilibrium, or parallel relaxation processes

sandpile model

randomly drop sand grains
if site reaches critical height., grains shift to neighbors
count how big “avalanches” are

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Per Bak, “How Nature Works,” 1996

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I II III IV

100 % Deterministic

100 % Stochastic

Mathematics

100

1000

Dimension - Physics

I. Solvable dynamic system, e.g. gear trains, physical pendulum

II. Amenable to perturbation theory, e.g. satellite orbits

III. Chaotic dynamic systems, e.g. climatology, Lorenz equations

IV. Turbulent/stochastic systems, e.g. quantum mechanics, turb. flow

(Source: Morrison, 1991)

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Three-Dimensional

Representation of

Action and Outcome

Events Over Time

In the Development

Of Cochlear Implant

Innovation

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# Dimensions

Time

Gestation Startup Begin Development End Development Implementation

Random

Chaotic

Periodic

Fixed Point

Random, Chaotic, and Periodic Dimensions

in the Innovation Journey

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Cycle 1:

Independent Company

Startups

Cycle 2:

Qnetics Merger

Cycle 3:

Load Management

Device

MICRO QNETICS ACTION AND OUTCOME EVENTS

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Cycling the Innovation Journey

Divergent Behavior

A branching & expanding process �of exploring new directions
Creating ideas & strategies
Learning by discovery
Pluralistic leadership
Building relationships and �porous networks
Creating Infrastructure �for collective advantage - Running in packs

Convergent Behavior

An integrating & narrowing process�of exploiting a given direction
Implementing ideas & strategies
Learning by testing
Unitary leadership
Executing relationships in �established networks
Operating within infrastructure �for competitive advantage

Enabling Factors

Resource Investments
Unit Restructuring

Constraining Factors

External rules and mandates
Internal focus and self-organizing

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