Stochastic analysis of the duration of the speaker role in psychotherapy

An analysis has been undertaken of the stochastic behavior of the time series which defines the duration of utterances exchanged by patients and therapists in six recorded sessions of psychotherapy. Each series followed a Box-Jenkins time series model of order (1, 0, 0): that is, each behaved as a first-order autoregressive process, sensitive to the prior state of the system. The confidences associated with the parameters of the autoregressive models were very high. In addition, the histograms of length of each utterance indicated an underlying Poisson model for the emergence of speech. The parameters of the Poisson and autoregressive models varied with each patient/therapist pair. Signatures for the process dynamics of the speaker-role variable were obtained. The two analyses suggest fundamental structures within the psychotherapeutic dialogue. The Box-Jenkins results provide a global summary of the inner structure of the series and its progression, while the Poisson results describe its instantaneous behavior. This work is offered as a part of new efforts to apply scientific and mathematical methods to the psychotherapeutic domain.