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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

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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 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 Theory formation Model building Empirical design Statistical methods

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Dynamic systems … 1

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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 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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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, … 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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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

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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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Dynamic systems of Development 8 Application of Dynamics to Social Sciences dynamic model of complex systems that are non-ergodic dynamic model of complex systems that are non-ergodic Explain complex system Explain ergodic

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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 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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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 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?

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Development … 2

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Dynamic systems of Development 12 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

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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 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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Dynamic systems of Development 14 What does development mean? (3) 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, ….

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Dynamic systems of Development 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) 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)

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Developmental mechanisms of change … 3

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Dynamic systems of Development 17 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)

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Dynamic systems of Development 18 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

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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,... 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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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 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 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 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 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 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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Applying dynamic systems to development …. 4

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Dynamic systems of Development 24 4 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

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Dynamic systems of Development 25 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)

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Dynamic systems of Development 26 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 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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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 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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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 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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Model building … 5

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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) 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 … 6

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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 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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Dynamic systems of Development 33 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

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Statistical Methods … 6

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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 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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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 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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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 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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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 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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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 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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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 Karnaugh maps Why: describing transitions through Boolean logic Who: Dumas et al, Schiepek, Tschacher example: mother-child interaction

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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) 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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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 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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Dynamic systems of Development 43 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 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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