Continuous Time Modeling in the Behavioral and Related Sciences

This unique book provides an overview of continuous time modeling in the behavioral and related sciences. It argues that the use of discrete time models for processes that are in fact evolving in continuous time produces problems that make their application in practice highly questionable. One main issue is the dependence of discrete time parameter estimates on the chosen time interval, which leads to incomparability of results across different observation intervals. Continuous time modeling by means of differential equations offers a powerful approach for studying dynamic phenomena, yet the use of this approach in the behavioral and related sciences such as psychology, sociology, economics and medicine, is still rare. This is unfortunate, because in these fields often only a few discrete time (sampled) observations are available for analysis (e.g., daily, weekly, yearly, etc.). However, as emphasized by Rex Bergstrom, the pioneer of continuous-time modeling in econometrics, neitherhuman beings nor the economy cease to exist in between observations.

In 16 chapters, the book addresses a vast range of topics in continuous time modeling, from approaches that closely mimic traditional linear discrete time models to highly nonlinear state space modeling techniques. Each chapter describes the type of research questions and data that the approach is most suitable for, provides detailed statistical explanations of the models, and includes one or more applied examples. To allow readers to implement the various techniques directly, accompanying computer code is made available online. The book is intended as a reference work for students and scientists working with longitudinal data who have a Master's- or early PhD-level knowledge of statistics.

Kees van Montfort is a professor of Quantitative Research Methodology at the Nyenrode Business Universiteit (Department of Marketing and Supply Chain Management) and a professor of Biostatistics at the Erasmus University Rotterdam (Department of Oncology). He is currently working on quantitative data analyses with researchers from several departments of the Nyenrode Business Universiteit and the Erasmus University Rotterdam. Additionally, he is pursuing the development of new statistical methods and techniques in the field of structural equation models, state space models and survival analysis.

Johan H.L. Oud is an associate professor at the Behavioural Science Institute of Radboud University, Nijmegen, the Netherlands, and visiting professor at Padjadjaran University, Bandung, Indonesia. His research interests are in family relations, structural equation modeling (SEM), longitudinal research, monitoring system construction, and continuous time analysis by means of SEM. He haspublished a series of papers and book chapters, and edited several books, in these fields.  He introduced the use of structural equation modeling into discrete-time and continuous-time state space modeling.

Manuel C. Voelkle is a professor of Psychological Research Methods at the Humboldt Universität zu Berlin and an adjunct researcher at the Max Planck Institute for Human Development. His research interests chiefly concern the design and analysis of multivariate empirical studies, with an emphasis on the use of structural equation models for the analysis of longitudinal data. Most of his methodological work addresses continuous time modeling and analyzing the intricate relationship of between- and within-person differences in psychological constructs as they evolve over time. He collaborates closely with other researchers in the study of developmental dynamics in affective and cognitive functioning.