Dynamic Systems methods
in the study of development
A practice-oriented approach
An introduction to the ISED Workshop on
Dynamic systems methods in development
Groningen, May 14-16 2007
Dynamics of Development: knowledge map
Dynamic systems
•What it is and what it is
not not
Development
•Basic components
•Basic mechanism(s)
Development and
dynamic systems
Empirical
design
Statistical
methods
Theory
formation
Application of dynamic
systems to development
Model
building
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1
Dynamic systems …
Dynamics: basic definition and properties
• an approach to the description and
explanation of change
• what it is not: misunderstandings in
social science
• it is not a model with time as predictor (as in
multilevel growth model, for instance)
• social science and psychology has focused on
static ergodic models
• whereas it should have been focusing on
dynamic non-ergodic models if it wants to really
understand change
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Two equations: the static and dynamic models
x t+1 = f ( x t )
Variable x
•
Give me a value of x and I will tell
Dynamic system:
x
=
f
(
x
)
t+1
t
you what the next value of x will
• The value of be
a variable x is a function of its
preceding state
The model generates a time
• Static system:series
x i = f ( y i)
• The value of a variable x
• Is a function of the variable y
• Or any set of such variables, ya, yb, yc, …
time
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xi=f(yi)
Variable x
Give me a value of y and I will tell
you what the corresponding
value of x will be
The model generates a
population sample
Variable y
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Dynamic system and geometric space
End
attractor
similarity
Example:
emergence of
friendship in
function of
mutual
preference and
similarity;
applies to
dyad
start
Mutual preference
wobbles, humps and sudden jumps - theoretica lreflection
7
Application of Dynamics to Social Sciences
• dynamic model
• of complex systems
• that are non-ergodic
Explain complex system
Explain ergodic
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ergodicity
• An informal definition
• Imagine a statistical analysis over the entire ensemble
of people at a certain moment in time
• and a statistical analysis for one person over a certain
period of time
• an ensemble is ergodic if the two types of statistics give
the same result, and non-ergodic if this is not so
• ergodicity hardly ever applies to behavioral
data!
• Molenaar
• considerable consequences for research methodology
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What is a complex system?
• A complex system is any system featuring
a large number of interacting components
(agents, processes, etc.)
• whose aggregate activity is nonlinear (not
derivable from the summations of the
activity of individual components)
• and typically exhibits … self-organization
…
• Rocha, 1999
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2
Development …
What does development mean? (1)
• meaning unwrapping
• like the unwrapping of a bookroll,
• notion of an inner logic in the sequence
• notion of finality
• life span more than just development
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What does development mean? (2)
• there's also education, learning and
teaching
• learning: having experiences that make
you change
• teaching: giving someone experiences that
make him change in a particular direction
• there is maturation and aging
• biologically governed processes of change,
including the aspects of rising and falling,
deterioration
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What does development mean? (3)
• developmental viewpoint: development is
the overarching term
• Encompassing learning, teaching, niche-seeking,
maturation, aging, ….
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The classical developmentalists’ view
• Piaget, Vygotsky, Wallon, Werner. …
• all changes of the system occur through
information that is "moderated" through the
system
• “moderated” means that
• the system encodes the information and adapts only in
function of this encoding (as in Piaget's assimilation and
accommodation)
• the system selects its own niche, i.e. preferred and
adapted environment (also biologically and geneticallyPlomin)
• the caring environment (educators, parents) adapt the
environment to the system's level and possibilities (as in
Vygotsky's ZPD)
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3
Developmental mechanisms
of change …
The basic mechanism (1)
• all changes of the system occur through
information that is "moderated" through
the system
• it is a fundamentally recursive notion
• next step is a function of the preceding step
• and thus a direct expression of a dynamics in
the fundamental sense (see basic definition)
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The basic mechanism (2)
• it is a fundamentally interactional notion
• the dynamics occurs through the interaction
with an environment or context
• this environment is of many kinds: biological,
spatial, cultural, ...
• a badly missing component: the utilitydriven nature of human action and the
motor of action and development
• biology and economics emphasize the utilitydriven nature of action
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The drive for developmental change (1)
• appears as a factor among many others:
motivation for instance
• relates to control theory, happiness/pleasure
theories; appraisal theory of emotion, selfactualization (Maslow), drives (Freud) ….
• but is far from the fundamental dynamic factor
that features in biology (fitness-maximization)
or economics (utility-drive)
• you need to understand the dynamics of the utility
function in order to understand the dynamics of the
long-term process, e.g. biological evolution, economic
processes and trade, ...
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The drive for developmental change (2)
• the dynamics of the utility function is
essential for understanding the shortterm dynamics of change
• the short-term dynamics of development
involves the dynamics of action
• see the model of interaction dynamics S and
VG
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Dynamic systems approach to
development (1)
• you can define an organism as a
manifold, a space of variables
• specify its changing position on a
developmental ruler
• Properties worth studying
• discontinuity next to continuity
• construction of novelty next to transmission and
appropriation
• Fuzziness and ambiguity
• intra-, inter- and contextual variability
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Dynamic systems approach to
development (2)
• A Dynamic Systems theory of
development incorporates
•
•
•
•
•
•
the basic recursive developmental mechanism
Interaction and transaction
Action drives, evaluation and control
Short-term dynamics of action
Long-term dynamics of development
Link between short- and long-term dynamics
• Serve as criteria for existing theories
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4
Applying dynamic systems to
development ….
4 areas of discussion
• Theory formation
• Existing theories
• Theories that await application to development
• Model building
• Empirical design
• Statistical methods
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Existing theories (1)
• qualitative use of complex dynamic
systems concepts
• Lewis, Fogel, Granic, Dishion, …
• theory of embedded-embodied action
• Thelen and Smith (Spencer, Schoner, ...)
• short-term interactional aspect of development:
organism-environment interaction
• development as change in the dynamic field
(Schoner)
• related theories: ecological psychology (Gibson)
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Existing theories (2)
• Connectionism
• Really a DST approach? Or are they
supplementary?
• Focuses on the organismic-brain component
• Dynamic growth theory
• Van Geert, Fischer, Case,language
development
• emphasizes long-term dynamics: growth as an
auto-catalytic process under limited resources
• related theories: biological theory of ecology
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Existing theories (3)
• theory of developmental dynamics
• Classical developmentalists (Van Geert
1998)
• based on the fundamental developmental
mechanisms in classical theories
• theory of dyadic agents
• highly developed in macro-social theory
• beginning application to development
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theories that await application to
development
• symbolic dynamics, categorical
dynamics
• their major advantage: they link categorical with
quantitative descriptions and modeling, a link
that is badly needed in developmental (and
clinical) psychology
• fuzzy control system dynamics
• control theory and theory of agents
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5
Model building …
model building
• connectionist modeling
• differential and difference models of
growth phenomena
• Growth models
• Interaction models (“The Mathematics of
Marriage”, Gottman et al.
• agent models
• cognitive simulation and AI-models
(Anderson, ACT)
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Empirical Design …
Empirical design (1)
• High-frequency, time-serial N=1 studies
• samples result as collections of time serial studies
• the time-serial study should capture the characteristic
dynamics at the time scale at issue (which longitudinal
studies nromally not do)
• Experiments as perturbations
• experimental studies in psychology involve specific
perturbations of an ongoing process
• the experimental manipulation must be studied timeserially, as a perturbation that is assimilated by the
process or to which the process accommodates
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Empirical design (2)
• mixed time-serial designs
• combination of time-serial, longitudinal and
cross-sectional
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Statistical Methods …
Overview of methods
• Standard statistical methods
• Statistical methods for non-linear time series
• Standard optimization techniques for curvefitting
• Analysis of categorical state spaces
• State space grids
• Karnaugh maps
• Finite state diagrams, Markov chains and tpatterns
• Monte Carlo tools for statistical simulation
• methods that await application to development
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standard statistical methods
• Why: analysis of sample predictions
based on dynamic models
• “Who”: standard statistical packages
• Example:
• dynamic model of dyadic play in children of
different sociometric statuses
• principal component analysis of dyadic conflict
trajectories
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statistical methods for non-linear time
series
• Why: statistical description and analysis
of time series
• Who: Molenaar, Hamaker, et al.
• Example:
• non-linear time-serial factor analysis
• See Hamaker’s workshop
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standard optimization techniques for
curve-fitting
• Why: fitting dynamic models in the form
of differential equations or maps
(difference equations) to data
• “Who”: standard fitting techniques
• Example:
• fitting growth models to data, qualitative and
quantitative fitting
• See Van Geert’s Workshop
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categorical analysis of state spaces (1)
• State space grids
• Why: describe transitions among categorical
states and finding categorical attractor states
• Who: Lewis, Hollenstein
• example:
• dyadic interactions among adolescents
• See Hollenstein’s workshop
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categorical analysis of state spaces (2)
• Karnaugh maps
• Why: describing transitions through Boolean
logic
• Who: Dumas et al, Schiepek, Tschacher
• example:
• mother-child interaction
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finite state diagrams, Markov chains and tpatterns
• Why: finding patterns in time series
• who: Magnusson; Markov chains,
• example:
• time patterns in teacher-child interactions
• See Van Geert’s workshop (if possible)
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Monte Carlo tools for statistical simulation
• Why: applicable to non-standard data
• “Who”:
• often used in biology, non-standard problems,
small sample problems etc.
• Manly; Todman and Dugard
• example:
• significant peaks in variability of langauge
production (time series)
• Significance testing of dynamic model of dyadic
play
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methods that await application to
development
• fuzzy logic and categorical methods
• why: behavioral data are categorical, but fuzzy
• Who: Zadeh, Ragin, Smithson, Verkuilen
• example:
• Emergence of linguistic categories in young children
• analysis of computer use in toddlers
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