Roelof B. Toonen, University of Groningen, University Medical Center Groningen (UMCG), Interdisciplinary Center Psychopathology and Emotion regulation (ICPE), The Netherlands
Klaas J. Wardenaar, University of Groningen, University Medical Center Groningen (UMCG), Interdisciplinary Center Psychopathology and Emotion regulation (ICPE), The Netherlands
Sonja L. van Ockenburg, University of Groningen, University Medical Center Groningen (UMCG), Interdisciplinary Center Psychopathology and Emotion regulation (ICPE), The Netherlands
Elisabeth H. Bos, University of Groningen, University Medical Center Groningen (UMCG), Interdisciplinary Center Psychopathology and Emotion regulation (ICPE), The Netherlands
Peter de Jonge, University of Groningen, University Medical Center Groningen (UMCG), Interdisciplinary Center Psychopathology and Emotion regulation (ICPE), The Netherlands

Abstract: Despite extensive research, the link between etiological factors and depression remains poorly understood. This may in part be due to a focus on strictly linear definitions of causality, derived at the group level. However, etiological relations in depression are likely to be dynamical, nonlinear and potentially unquantifiable with traditional statistics. Therefore the aim of this study was to evaluate the use of the convergent cross-mapping (CCM) method in investigating possible nonlinear relationships between supposed etiological factors and depressive symptomatology. Time series data from six healthy individuals were used to model the relationship between 24-h urinary free cortisol and negative affect using CCM and dewdrop embeddings. CCM is a nonlinear measure of causality, based on state space reconstruction with lagged coordinate embeddings. The results showed that nonlinear dynamical relationships between cortisol and negative affect may be present within participants, as demonstrated by a positive cross-map convergence from negative affect to cortisol. However, analyses also showed that noise and influential points had considerable impact on the results. Convergent crossmapping can be used to reveal possible nonlinear dynamical relationships between etiological factors and psychopathology that may remain undetected with traditional linear causality measures.

Keywords: depressive symptomatology, nonlinear dynamical systems, CCM, time series, negative affect