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

With the increasing use of real-time monitoring procedures in clinical practice, psychological time series become available to researchers and practitioners. An important interest concerns the identification of pattern transitions which are characteristic features of psychotherapeutic change. Change Point Analysis (CPA) is an established method to identify the point where the mean and/or variance of a time series change, but changes of other and more complex features cannot be detected by this method. In this study, an extension of the CPA, the Pattern Transition Detection Algorithm (PTDA), is optimized and validated for psychological time series with complex pattern transitions. The algorithm uses the convergent information of the CPA and other methods like Recurrence Plots, Time Frequency Distributions, and Dynamic Complexity. These second level approaches capture different aspects of the primary time series. The data set for testing the PTDA (300 time series) is created by an instantaneous control parameter shift of a simulation model of psychotherapeutic change during the simulation runs. By comparing the dispersion of random change points with the real change points, the PTDA determines if the transition point is significant. The PTDA reduces the rate of false negative and false positive results of the CPA below 5% and generalizes its application to different types of pattern transitions. RQA quantifiers also can be used for the identification of nonstationary transitions in time series which was illustrated by using Determinism and Entropy. The PTDA can be easily used with Matlab and is freely available at Matlab File Exchange (https://www.mathworks.com/matlabcentral/fileexchange/80380-pattern-transition-detection-algorithm-ptda).

The identification of critical fluctuations and phase transitions in short term and coarse-grained time series-a method for the real-time monitoring of human change processes

We introduce two complementary measures for the identification of critical instabilities and fluctuations in natural time series: the degree of fluctuations F and the distribution parameter D. Both are valid measures even of short and coarse-grained data sets, as demonstrated by artificial data from the logistic map (Feigenbaum-Scenario). A comparison is made with the application of the positive Lyapunov exponent to time series and another recently developed complexity measure-the Permutation Entropy. The results justify the application of the measures within computer-based real-time monitoring systems of human change processes. Results from process-outcome research in psychotherapy and functional neuroimaging of psychotherapy processes are provided as examples for the practical and scientific applications of the proposed measures.