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
Dynamic systems of Development
2
Dynamics of Development: knowledge map
Development and
dynamic systems
Dynamic systems
•
What it is and what it is
not not
Development
•
Basic components
•
Basic mechanism(s)
Application of dynamic
systems to development
Theory
formation
Model
building
Empirical
design
Statistical
methods
Dynamic systems …
1
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4
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
•
Dynamic system: x
t+1
= f ( x
t
)
•
The value of a variable x is a function of its
preceding state
•
Static system: x
i
= f ( y
i
)
•
The value of a variable x
•
Is a function of the variable y
•
Or any set of such variables, y
a
, y
b
, y
c
, …
x
t+1
= f ( x
t
)
time
Variable x
Give me a value of x and I will tell
you what the
next
value of x will
be
The model generates a
time
series
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x
i
= f ( y
i
)
Variable y
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
wobbles, humps and sudden jumps

theoretica lreflection
7
Dynamic system and geometric space
Mutual preference
similarity
start
End
attractor
Example:
emergence of
friendship in
function of
mutual
preference and
similarity;
applies to
dyad
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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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•
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
What is a complex system?
Development …
2
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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 genetically

Plomin)
•
the caring environment (educators, parents) adapt the
environment to the system's level and possibilities (as in
Vygotsky's ZPD)
Developmental mechanisms
of change …
3
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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 utility

driven nature of human action and the
motor of action and development
•
biology and economics emphasize the utility

driven 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, self

actualization (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
short

term 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
Applying dynamic systems to
development ….
4
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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
Model building …
5
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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)
Empirical Design …
6
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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 time

serially, 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
Statistical Methods …
6
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Overview of methods
•
Standard statistical methods
•
Statistical methods for non

linear time series
•
Standard optimization techniques for curve

fitting
•
Analysis of categorical state spaces
•
State space grids
•
Karnaugh maps
•
Finite state diagrams, Markov chains and t

patterns
•
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 t

patterns
•
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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