Systems Methods for Developmental Research

Abstract

Abstract In this chapter a broad variety of aspects of dynamic systems approaches is discussed, including heuristic descriptions of methodological issues, experimental designs, mathematical models associated with such approaches and, in particular, statistical methods to fit dynamic systems models to appropriate empirical data. The authors start with a breakthrough in statistical modeling that has fundamental consequences for developmental science. It is shown that a general mathematical theory, called ergodic theory, puts dynamic systems approaches at the center of statistical modeling in developmental science. A general dynamic factor model is presented, which captures most of the statistical models that are appropriate in linear dynamic systems approaches. It is shown how specific variants of dynamic factor models enable critical tests of key characteristics of developmental processes. The chapter continues with an extensive discussion of the implications of nonlinear dynamic systems approaches for an important topic in developmental science: the analysis of stage‐wise development. Special emphasis is given here to neural network models and dynamic systems models based on catastrophe theory. The chapter closes with a heuristic presentation of mathematical control theory of dynamic systems as an important tool for optimal guidance of developmental processes.