dynamic systems methods in the study of development a practice-oriented approach an introduction to...

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 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 mapDynamics of Development: knowledge map

Development and dynamic systems

Development and dynamic systems

Dynamic systems•What it is and what it is not not

Dynamic systems•What it is and what it is not not

Development•Basic components•Basic mechanism(s)

Development•Basic components•Basic mechanism(s)

Application of dynamic systems to development

Application of dynamic systems to development

Theory formation

Theory formation

Model building

Model building

Empirical design

Empirical design

Statistical methods

Statistical methods

Dynamic systems …

1


Dynamics: basic definition and propertiesDynamics: 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

• 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


Two equations: the static and dynamic modelsTwo 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, ya, yb, yc, …

• 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, ya, yb, yc, …

x t+1 = f ( x t )x t+1 = f ( x t )

time

Var

iabl

e x

Give me a value of x and I will tell you what the next value of x will be

Give me a value of x and I will tell you what the next value of x will be

The model generates a time seriesThe model generates a time series


x i = f ( y i )x i = f ( y i )

Variable y

Var

iabl

e x

Give me a value of y and I will tell you what the corresponding value of x will be

Give me a value of y and I will tell you what the corresponding value of x will be

The model generates a population sampleThe model generates a population sample

wobbles, humps and sudden jumps - theoretica lreflection 7

Dynamic system and geometric spaceDynamic system and geometric space

Mutual preference

sim

ilari

ty

start

End attractor

Example: emergence of friendship in function of mutual preference and similarity; applies to dyad


Application of Dynamics to Social SciencesApplication of Dynamics to Social Sciences

• dynamic model

• of complex systems

• that are non-ergodic

• dynamic model

• of complex systems

• that are non-ergodicExplain complex system

Explain complex system

Explain ergodicExplain ergodic


ergodicityergodicity

• 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

• 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


• 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

• 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?What is a complex system?

Development …

2


What does development mean? (1)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

• 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



• 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

• 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



• developmental viewpoint: development is the overarching term• Encompassing learning, teaching, niche-seeking,

maturation, aging, ….

• developmental viewpoint: development is the overarching term• Encompassing learning, teaching, niche-seeking,

maturation, aging, ….


The classical developmentalists’ viewThe 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)

• 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


The basic mechanism (1)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)

• 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)


The basic mechanism (2)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

• 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


The drive for developmental change (1)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, ...

• 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, ...


The drive for developmental change (2)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

• 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 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

• 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




• 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

• 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


4 areas of discussion4 areas of discussion

• Theory formation• Existing theories• Theories that await application to development

• Model building

• Empirical design

• Statistical methods

• Theory formation• Existing theories• Theories that await application to development

• Model building

• Empirical design

• Statistical methods


Existing theories (1)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)

• 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)



• 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

• 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



• 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

• 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


theories that await application to developmenttheories 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

• 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


model buildingmodel 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)

• 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


Empirical design (1)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

• 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


Empirical design (2)Empirical design (2)

• mixed time-serial designs• combination of time-serial, longitudinal and

cross-sectional

• mixed time-serial designs• combination of time-serial, longitudinal and

cross-sectional

Statistical Methods …

6


Overview of methodsOverview 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

• 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


standard statistical methodsstandard 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

• 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


statistical methods for non-linear time seriesstatistical 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

• Why: statistical description and analysis of time series

• Who: Molenaar, Hamaker, et al.

• Example: • non-linear time-serial factor analysis• See Hamaker’s workshop


standard optimization techniques for curve-fittingstandard 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

• 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


categorical analysis of state spaces (1)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

• 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


categorical analysis of state spaces (2)categorical analysis of state spaces (2)

• Karnaugh maps• Why: describing transitions through Boolean

logic• Who: Dumas et al, Schiepek, Tschacher• example:

• mother-child interaction

• Karnaugh maps• Why: describing transitions through Boolean

logic• Who: Dumas et al, Schiepek, Tschacher• example:

• mother-child interaction


finite state diagrams, Markov chains and t-patternsfinite 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)

• Why: finding patterns in time series

• who: Magnusson; Markov chains,

• example:• time patterns in teacher-child interactions• See Van Geert’s workshop (if possible)


Monte Carlo tools for statistical simulationMonte 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

• 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


methods that await application to developmentmethods 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

• 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

dynamic systems methods in the study of development a practice-oriented approach an introduction to...

Documents

dynamic modelsdynamic

dynamic nonergodic models

development mean

preceding statestatic

static ergodic modelswhereas

statistical analysis

variable xis

variable yor