136 Chapter 6 from one day until the next (lag-1 association). Due to the number of repeated bivariate associations we evaluated significance at p < 0.01. 2.4.3 Change-mechanisms For the third and last step we analyzed temporal instability and pinpointed extraordinary events, to obtain insight into potential change-mechanisms (i.e., either instability-induced, event-induced or both). The (in)stability of daily self-ratings was analyzed with dynamic complexity (Schiepek & Strunk, 2010) as implemented in R-package casnet (Hasselman, 2023). Dynamic complexity is comprised of a multiplication between distribution measure D, which reflects the distribution uniformity of data-points within the range of the used scale, and fluctuation measure F, which indicates the strength and number of fluctuations within the timeseries. As such, it is more robust to non-stationarity and periodicity than alternative measures such as variance (cf Olthof et al., 2020b; Schiepek & Strunk, 2010). Because dynamic complexity cannot handle missing data, we first employed Kalman smoothing with the na_kalman function (Moritz & BartzBeielstein, 2017) to impute missing data-points using a structural model fitted by maximum likelihood. Dynamic complexity can only be computed for ordinal or continuous timeseries (Schiepek & Strunk, 2010), hence dynamic complexity could not be computed for the binary variables aggressive and self-injury incidents. Instead, dynamic complexity was calculated on the most relevant six-point scale items: “urge for aggression” and “urge for self-injury”, each within a sevenday backwards overlapping window. This window shifts gradually along the timeseries without changing in width, such that dynamic complexity is first calculated for each item between day 1 and day 7, then between day 2 and day 8, and so on. With this 7-day window we again control for day-of-the-week effects. The windowed dynamic complexity was visualized on a timeline per item. A one-tailed z test (α = 0.05) was applied on each dynamic complexity timeline to determine at which time-windows there was significant instability (i.e., high dynamic complexity). We chose to perform a one-tailed significance test because we wanted to examine the occurrence of high dynamic complexity values (not low values), exceeding the threshold of the average dynamic complexity (cf. Fartacek et al., 2016; Olthof et al., 2020b; Schiepek et al., 2016). We ultimately described, per identified transition, whether it was preceded or accompanied by significant instability and/or an extraordinary event. These extraordinary events were codes categorized into subthemes during the thematic analysis procedure. That is, after the coders had familiarized themselves with the data, generated and discussed initial codes they reached consensus about which events reflected everyday events and which events were extraordinary across the 560 day period. In the absence
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