Convergent Validation of Methods for the Identification of Psychotherapeutic Phase Transitions in Time Series of Empirical and Model Systems

Abstract

In many cases, the dynamics of psychotherapeutic change processes is characterized by sudden and critical transitions. In theoretical terms, these transitions may be "phase transitions" of self-organizing nonlinear systems. Meanwhile, a variety of methods is available to identify phase transitions even in short time series. However, it is still an open question if different methods for timeseries analysis reveal convergent results indicating the moments of critical transitions and related precursors. Methods and Procedures: Seven concepts which are commonly used in nonlinear time series analysis were investigated in terms of their ability to identify changes in psychological time series: Recurrence Plots, Change Point Analysis, Dynamic Complexity, Permutation Entropy, Time Frequency Distributions, Instantaneous Frequency, and Synchronization Pattern Analysis, i.e., the dynamic inter-correlation of the system's variables. Phase transitions were simulated by shifting control parameters in the Hénon map dynamics, in a simulation model of psychotherapy processes (one by an external shift of the control parameter and one created by a simulated control parameter shift), and three sets of empirical time series generated by daily self-ratings of patients during the treatment. Results: The applied methods showed converging results indicating the moments of dynamic transitions within an acceptable tolerance. The convergence of change points was confirmed statistically by a comparison to random surrogates. In the three simulated dynamics with known phase transitions, these could be identified, and in the empirical cases, the methods converged indicating one and the same transition (possibly the phase transitions of the cases). Moreover, changes that did not manifest in a shift of mean or variance could be detected.

Studying Behaviour Change Mechanisms under Complexity

“…In clinical psychology, intensive monitoring of psychopathological symptoms has allowed researchers to examine symptoms’ variability, autocorrelations and other indicators of dynamics during interventions. This has yielded considerable advances in the prediction of phase transitions between adaptive and maladaptive psychological states [ 58 , 126 , 127 , 128 ]. A conceptual replication in a population undergoing a weight loss intervention [ 129 ] recently found that sudden drops in physical activity levels could be predicted by the emergence of erratic fluctuations in day-to-day physical activity.…”

Detecting pattern transitions in psychological time series – A validation study on the Pattern Transition Detection Algorithm (PTDA)

“…It should be noted that long-term predictions are impossible in complex nonlinear systems, but with regard to short-term predictions, several indicators of qualitative changes of a system have been identified. Therefore, researchers and therapists will not be successful in long-term forecasting of specific trajectories of change, but should be vigilant to the possibility of transition points of the system [26]. Such transitions from one pattern to another are called phase transitions [24].…”

“…A variety of measures to determine the point at which a system changes its qualitative behavior exist in various disciplines like climate research, physics, ecology, neuroscience, and physiology (e.g., [28][29][30], see [26] for an overview). A commonly used method in psychology but also in other research areas is the Change Point Analysis [31], which is available in softwares like R and Matlab.…”

“…Change Point Analysis can then be applied not only to detect changes of the primary time series, but also to detect changes of the distribution, frequency, and recurrent patterns. Using information from various secondary measures increases the validity of the location of change [26].…”

“…Compared with the first description of the algorithm [26], we illustrate in the present paper not only the feasibility of applying the PTDA to some simulated and empirical data, but conduct a systematic validation of the algorithm by using 300 simulated time series. Furthermore, we optimized the algorithm.…”