Synchrony
As we already reported in Sect.8.3, in recent years an empiricalfield has evolved in psychotherapy that explores the manifestation of synchronization, or in short syn- chrony, in the psychotherapy setting. As we have shown in Sect.8.2, synchrony results from the coupling terms of the minimal model we introduced in Sect.8.1, axclxthandbx2th. In order to be able to simplify the equations of the minimal model proposed there, we assumed to choose the coupling constantsasmall andb>0.
In this chapter, we report on methodological avenues to estimate the coupling terms of therapeutic interactions from empirical time series. The goal of this research was generally twofold. First, as a“proof of existence,”it was necessary to show that coupling existed at all, i.e., to show that the assumptiona,b>0 could be supported against control conditions. Second, several studies explored the functionality of synchrony with respect to outcome. A review of this research is given by Koole and Tschacher (2016). We will not go into the second point here, but focus on the methods—how can we explore the assumption of coupling between therapist and client based on empirical measurements?“Proof of existence”of therapeutic syn- chrony means that we wish to support or refute the claim that therapist and client behavior is synchronized.
Algorithms that estimate synchrony address the coupling betweenxclandxth. In contemporary psychotherapy research, these state variables commonly consist of measurements, which were sampled at high frequency (exceeding 1 Hz) and which cover time spans of sufficient duration, usually spanning at least 5 min; time spans can go up to the length of whole therapy sessions, hence about 50 min. In much recently published research, the type of data covered by the state variables was simultaneously occurring movement behavior, which can be conveniently sampled
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by video analysis, actigraphy, or motion tracking of therapists’and clients’motor behavior. The resulting synchrony is commonly termed nonverbal synchrony or movement synchrony.
Further appropriate state variables are physiological signals simultaneously monitored from therapist and client in a session (Tschacher and Meier, 2019).
Most frequently, electrodermal activity was recorded by electrodes placed on thefingers (Coutinho et al.,2018), and sometimes respiration activity was sampled by breathing belts attached to the chests or electro-cardiac parameters using photoplethysmography. The hyperscanning procedures based on electroencephalo- graphic variables are rare in this research because of the vulnerability for motion artifacts.
Here we will not discuss the various psychological meanings of each of these different types of data. It may suffice to say that nonverbal movement may be seen as an expression of“body language”conveying social information, whereas physio- logical activity is closely connected to emotional experiencing.
Synchrony computation processes two-dimensional datasets, and most methods function within the time domain using windowed cross-correlations (WCC) of the paired time series (Fig.9.5).
We now describe an approach for the computation of synchrony using WCC and surrogate controls (surrogate synchrony, SUSY, cf. www.embodiment.ch). SUSY derives the cross-correlations segment-wise—time series are cut into segments of, for example, 50 s, and the cross-correlations within each segment are computed within a certain range of lagsL. A default value in many studies is that lags up to 5 s (5 sL5 s) are chosen, i.e., all cross-correlations within a 10-s window are considered. In the examples in Figs. 9.5,9.6, and9.7, we chose 4 sL 4 s.
Thus, segment-size and window-size are basic parameters that have to befixed in Fig. 9.5 The windowed cross-correlation (WCC) function of two time seriesXcl,Xth. The time series are segmented (segments 1 to 8 of the therapist data and 1* to 8* of the client), the cross- correlation function is computed in each segment (i.e., in 1;1*, 2;2*, etc.), aggregated per lagLin each segment, then aggregated a second time over all segments of the time series, and then depicted as an overall cross-correlation function of the two time series (right panel)
SUSY. Synchrony can then be defined as the aggregated sum of all these cross- correlations. This operationalization thus includes the simultaneous (lag 0) correla- tion as well as time-lagged correlations. The time-lagged correlations cover all other lags within the window signifying responses of therapist to client as well as responses of client to therapist. WCC represents a default procedure used in most Fig. 9.6 The windowed cross-correlation function (WCC) of surrogate time series ofXcl,Xth. The surrogate cross-correlation function is computed in shuffled segments (in the example 1;2*, 2;3*, 3;6*, 4;7*, etc.). After aggregation, a surrogate cross-correlation function is generated (right panel)
Fig. 9.7 The result of SUSY is the effect size ESsythat expresses the degree to which the empirical cross-correlation function (Fig.9.5) exceeds the surrogate cross-correlation function (Fig.9.6). ESsy corresponds to the area under the green curve minus the area under the red curve, divided by the standard deviation of the surrogates
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previous research (Tschacher et al., 2014). All cross-correlations are transformed using Fisher’s Z transformation; the absolute Z values are aggregated separately in each segment of the entire time series. Finally the aggregated Z values of all segments are averaged across the entire time series to obtain a value of synchrony for the therapist-client dyad,Zreal.
A subsequent step in studies applying SUSY consists of surrogate tests (Moulder et al., 2018; Ramseyer & Tschacher, 2010). Surrogate time series can serve as a control condition for the aggregatedZ values produced by WCC. Surrogates of a single dataset can be obtained by the random shuffling of the single segments of the time series (see Fig.9.6): when a two-dimensional time series containsnsegments, n(n1) permutations can be realized, each forming a time series in which therapist and client data are however falsely arranged with respect to simultaneity, but the mean as well as standard deviation and other characteristics of the time series are preserved. Thus, segment-shuffled surrogates provide a good control condition.
WCC is then run on all n (n1) surrogates, and the effect size ESsyof“real” synchrony Zreal with respect to averaged“false”surrogate synchrony Zsurr can be computed using the standard deviation (SD) of“false”surrogate synchronies, hence ESsy¼ ZrealZsurr
=SDðZsurrÞ. The effect size ESsy can be visualized as the area between the curves in Fig. 9.7. We abbreviate this two-step algorithm for the computation of synchrony using WCC and surrogate controls by the acronym SUSY.
We developed a further algorithm for the time domain, which is based on the correlations of local slopes instead of the cross-correlations, providing a concor- dance index(CI, cf.www.embodiment.ch). A simple version of the CI was previ- ously developed and used to assess physiological synchrony by Marci and Orr (2006) and Karvonen et al. (2016). The CI computes synchrony via correlations of window-wise slopes of a two-dimensional time series that contains a series A with therapist data and a series B with client data. All slopes of A and B are determined in the following manner: define as a parameter the window-size (e.g., 2 s) and, as a further parameter, the segment-size (e.g., 10 s). Then a slope (using mean squares regression lines) is computed for A and B inside thefirst window of segmentn, the window is shifted by 1 s, and the slopes are again computed, until all windows in segmentnare considered. The slopes in segmentnof time series A are correlated with those in the same segment of B. The principle of this approach is illustrated in Fig.9.8.
The procedure is repeated until all segments of A and B are considered. All correlations are transformed to Fisher’s Z correlations, and the mean Z of the two-dimensional time series is computed. This procedure and the segment-wise shuffling used to create surrogate time series are performed in analogy to the method described above for SUSY, yieldingZ0realand ES0sy.
The CI of a segment is defined by the natural logarithm of the sum of all positive correlations divided by the absolute value of the sum of all negative correlations. The CI of the complete time series is defined by the average over all segments, thus CI.
Using segment shuffling, an effect size ES CI
is computed in the same manner as detailed above for SUSY.
Before we focus on empirical assessments in the next section, let us briefly address the limitations to these empirical applications. In all naturalistic time series, the functions K(x) andQ(x) will not be as well-behaved as can be expected from Fig. 9.4, simply because some assumptions for the time series will not be met.
Especially in psychotherapy research, the time steps of measurement cannot be arbitrarily small because a minimum temporal distance between measurements must be obeyed. Also, the number of empirical measurements can, for practical reasons, not be arbitrarily large. In addition, the longer the time period of measure- ment, the more likely there will be parameter changes and context variation, so that the stationarity of the time series may no longer be given. Finally, in empirical psychotherapy research one is often confronted with scaling issues—data originating from questionnaire scales have discrete steps as was reported in Sect.1.2. Therefore, discrete and truncated time series will generate noncontinuous results so that we will have to live with non-differentiable functions and we may have to approximate the continuous curves.
Fig. 9.8 The principle of the concordance index (CI) algorithm. In segments of time series A and B, the local slopes of regression lines (black) are computed in all windows that cover the segment. The CI is based on the correlations of the slopes of A with those of B
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