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
Dynamic systems of Development
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
Dynamic systems of Development
5
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
Dynamic systems of Development
6
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
Dynamic systems of Development
8
Application of Dynamics to Social Sciences
•
dynamic
model
•
of
complex
systems
•
that are
non

ergodic
Explain
complex system
Explain
ergodic
Dynamic systems of Development
9
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
Dynamic systems of Development
10
•
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
Dynamic systems of Development
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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
Dynamic systems of Development
13
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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15
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
Dynamic systems of Development
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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)
Dynamic systems of Development
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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
Dynamic systems of Development
19
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, ...
Dynamic systems of Development
20
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
Dynamic systems of Development
21
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
Dynamic systems of Development
22
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
Dynamic systems of Development
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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)
Dynamic systems of Development
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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
Dynamic systems of Development
27
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
Dynamic systems of Development
28
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
Dynamic systems of Development
30
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
Dynamic systems of Development
32
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
Dynamic systems of Development
33
Empirical design
(2)
•
mixed time

serial designs
•
combination of time

serial, longitudinal and
cross

sectional
Statistical Methods …
6
Dynamic systems of Development
35
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
Dynamic systems of Development
36
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
Dynamic systems of Development
37
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
Dynamic systems of Development
38
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
Dynamic systems of Development
39
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
Dynamic systems of Development
40
categorical analysis of state spaces
(2)
•
Karnaugh maps
•
Why: describing transitions through Boolean
logic
•
Who: Dumas et al, Schiepek, Tschacher
•
example:
•
mother

child interaction
Dynamic systems of Development
41
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)
Dynamic systems of Development
42
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
Dynamic systems of Development
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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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