Keatley, D. A1. and Clarke, D. D.2
1Researchers in Behaviour Sequence Analysis (ReBSA) and University of Lincoln, LN6 7TS.
2Researchers in Behaviour Sequence Analysis (ReBSA) and University of Nottingham, NG7 2RD.
The traditional approach to research in Psychology has been to use cross-sectional designs. While temporal methods are not new, they are relatively under-used; however, researchers have been developing methods to analyse temporal dynamics [1 - 3]. Mapping changes in behaviour over time facilitates understanding of causal effects and predicting of future outcomes. To date, there are several main approaches to analysing the influence of variables over time in dynamic systems: Survival Analysis [4 - 5]; Behaviour Sequence Analysis [3], T-Pattern Analysis [6 - 7]; and temporal Social Network Analysis [8 - 9]. All of these methods have proven hugely beneficial in mapping the effects of multiple antecedent factors leading toward different outcomes. The aim of the current presentation is to offer a novel method of temporal measurement, Indicator Waves, which allow multiple simultaneous and sequential events to be analysed across varying time-spans. Indicator waves provide easy-to-read statistical wave diagrams, which are interpretable by a wide range of non-specialist end-users. The waves provide quick inference about which risk factors, behaviours, or events (termed ‘Indicators’) are prevalent across different points in time. The plots at each time point provide a profile of the absence or presence of indicators at that time. The method can be applied to both human and non-human samples.
Understanding the temporal effects of different indicators can provide important insight into the fluctuations of different events across time. For instance, if a researcher were attempting to forecast the next episode of relapse in addictions or self-harm [3, 10, 11], knowing the effects of intrapersonal and interpersonal factors in the preceding minutes, hours, days, weeks, or even months, might allow better prediction of
subsequent relapses or episodes. Traditionally, longitudinal studies have attempted to provide this sort of
information; however, longitudinal studies incur the limitation of sample drop-out, or having to wait an unknown length of time until relapse (which might never occur!). These limitations are well-known and considered a worthwhile hurdle in order to gain longitudinal data. Some research designs make use of existing, legacy datasets, which removes some of the issues of longitudinal research; however, such datasets can be hard to access or miss key variables that limit the research. A further limitation of temporal analyses, such as Survival Analysis, is that accounting for multiple behaviours across time is not easily possible. A method is required, therefore, that allows for temporal dynamics to be analysed, across multiple indicators.
Behaviour Sequence Analysis (BSA) methods offer researchers the opportunity to measure the relationship between multiple behaviours across time [3]. BSA is based on mathematical Markov models, which analyse the transitions between one event, the antecedent, on a following event, the sequitur. Complex chains of events are then developed to show how A leads to B, B leads to C and so forth. Lag-Sequence Analysis (LSA), which is the most typical form of BSA, typically involves analysing the effect of an antecedent on a sequitur [3, 12 - 13]. The analyses does allow for longer chains to be built, or more distal lags to be measured; however, the underlying focus is on the transition relationships between antecedents and sequiturs. This method has proven useful in a number of domains. The analysis is possible; but, can lead to a combinatorial explosion in analyses [13].
T-Pattern Analysis (TPA) has been proposed, therefore, to overcome the limitations of traditional LSA approaches. TPA allows for complex patterns of sequential and concurrent behaviours to be analysed, and hierarchical patterns to emerge. This method allows for timing of sequential and hierarchical events to be mapped in a dataset, showing fractal dimensions, which can increase prediction of future events [7]. Some of the limitations in Lag-Sequence Analysis are, therefore, overcome with TPA. However, TPA is a much more complex form of analyses, and can require additional training to run and interpret analyses. While the ‘pay-off’
for understanding such analyses is worthwhile, it can be restrictive to some audiences.
A method is clearly needed, therefore, which brings together the benefits of temporal analyses with multiple events. The method should allow for outputs that can be easily followed and understood, while also allowing multiple concurrent and sequential behaviours to be mapped. Indicator Waves provides all of these strengths, without any of the limitations. Indicator Waves allow multiple behaviours and events to be analysed at varying time scales to be measured at different points in time. The analyses can run on very short timescales (e.g., milliseconds) through to life-history timelines. The output of analyses are waves that outline how likely (or unlikely) the occurrence of indicators are at each time point. End-users can read waves across the graph to see when and where they fluctuate, the Indicator Waves diagram can also be interpreted as ‘profiles’ at particular time points, indicating which events are likely to occur at that time point, and which are less likely to occur.
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The Indicator Waves Method
The first stage for researchers is to define the various indicators that they want to measure or map over a time course. This stage is analogous to creating the behaviour list in BSA research [3]. As with BSA, it may be that researchers define the indicators, a priori, or post hoc; however, ensuring a complete list is developed increases clarity and precision of results. The next step is to decide on the time scale and intervals used to measure the indicator waves across. A coarse time-scale with large intervals may be better suited to life history research; however, smaller intervals can be used for smaller time-scales (e.g., nonverbal communication and micro-gestures). The timeline may also be compressed and elongated depending on research-relevant question that may be of interest. For example, as an outcome event nears, it may be important to investigate the
fluctuations of indicators on smaller time scales. It is possible, therefore, to have a timeline that has indicators at monthly ‘check-ups’ or points in time; however, in closer proximity to the outcome event, the timeline may include weekly, daily, or even hourly inputs. The analyses can be ‘zoomed in’ or ‘zoomed out’ of particular time points, to show greater clarity in indicator fluctuations.
Data may be gained from a variety of sources, as with BSA research [3]. Existing, legacy datasets or sources may be used and coded, in written, spoken, or video form. Similarly, researchers may conduct cross-sectional studies, asking participants to recount their previous behaviours and experiences of indicators in the past. Finally, researchers may wish to conduct a longitudinal design with Indicator Waves (or include an Indicator Waves questionnaire in their existing longitudinal research). The Indicator Waves questionnaire is relatively straightforward and simple to design, and can be administered via pen-and-paper, or online questionnaire sites and mobile apps. An example of an Indicator Waves questionnaire is given in Figure 1.
Figure 1. Indicator Waves Questionnaire. The Indicators in column 1 are typically much longer lists, involving events, behaviours, or cognitions. The timeline can have greater or shorter intervals, depending on research questions. This example is for an Indicator Waves project predicting an outcome behaviour, it is not always necessary to have an outcome, per se – the method can be used to map trajectories of indicators across time (e.g.,
across an expedition or treatment programme) Analyses
Similar to traditional BSA research [3], the first step in Indicator Waves analysis is to gain an insight into the raw frequencies of individual indicators in the dataset. This most closely corresponds to previously conducted research on known risk factors and variables associated with an outcome, it also provides end-users with an initial insight into which indicators occur most or least frequently in the dataset. Frequencies can be globally calculated – across the entire timeline, or can be calculated at each time point. The analysis of
frequencies is a simple first step; however, further analyses are required to fully understand the distribution and likelihood of events occurring.
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Indicator Waves
Chi-square analysis of the Indicator Waves frequency matrix shows standardised residuals (SR), which are the preferred analysis approach in Indicator Waves, for the same reasons as given in BSA research [3].
Standardised residuals show which indicators are occurring more times, or fewer times than expected by chance at each time point. A higher SR means that an indicator is occurring more than would be expected by chance, at a particular time point. In contrast, a negative SR shows than an indicator is occurring fewer times than would be expected by chance, at a time point. A table can be developed of SRs to show indicators x time points, which is similar to the transition frequency matrix produced in BSA research [3]
Table 1. Standardised Residual Matrix (segment from a larger database). Values are standardised residuals (SRs).
Positive values show each indicator event occurs more likely than would be expected by chance, at a particular time point. Negative values that the indicator event occurs less likely than would be expected by chance, at that
time point. The final column indicates this timeline continued across many more previous time points.
The table provides the complete results for all indicators, at each time point. However, for larger tables, interpreting the table and understanding the combined presence or absence of a number of indicators, across different time points would be extremely difficult. Therefore, the next stage of Indicator Waves is to produce a diagram of the waves, which can be more easily interpreted. The diagram (see Figure 2) shows how different indicators are present or absent at different time points.
The Indicator Waves diagram can be very simply read and understood by individuals without advanced statistical training, making it ideal for applied use. The lines show which indicators (Felt depressed;
Felt angry etc.) occur at different points in time. Depression, for instance, is likely to occur throughout each time point; however, peaks at around a month prior to the predicted outcome event. Anger (Felt angry) peaks an hour before the outcome; but, dips and is absent a week and a month prior to the outcome event. Each plot along
the x-axis indicates a specific point in time, and shows how indicators may be present or absent at different times in the build-up to an outcome.
Each point on the x-axis is akin to a profile at that point in time. Therefore, an individual experiencing
no despair; but, experiencing anger, anxiety, and depression is likely to be in the ‘previous 1 hour’ point. Similarly, an individual without pessimism; but, increased levels of depression and despair, is likely to b at the ‘3 months ago’ time point. This has a clear clinical application, and advanced statistical approaches are developed to provide an index of matching new cases to known cases in a database.
Figure 1. Indicator Waves diagram. Timeline order has been switched from Table 1, to represent passage of time.
This is a segment of a longer timeline dataset (spanning many months).
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Discussion and Conclusions
A limitation of previous time-series analysis methods has been the complexity of outcomes when multiple concurrent and sequential events are plotted [3]. A primary aim of applied research should be to develop methods that can be interpreted by lay audiences, without statistical backgrounds. State Transition Diagrams, for instance, are simplified models of complex datasets, which allow individuals to follow chains of behaviour [3, 13]. Although concurrent behaviours can be analysed in BSA, this typically leads to very complex analyses and outputs. For example, from a simple ABC chain, multiple groupings can be made (i.e., [AB;
AC, BC, ABC, ABC etc.), rendering the simplified State Transition Diagrams prohibitively complex to read. The current Indicator Waves approach, however, allows for complex datasets of sequential and concurrent events to be analysed and plotted in simplified diagrams.
A further benefit of the Indicator Waves approach is the possibility of matching cases to existing datasets. Each time point in the Indicator Waves approach offer a profile of the typical presence or absence of indicators at that point in time. When a new case emerges, further analyses can be conducted to investigate which profile point in time it most closely matches. This offers researchers and practitioners the ability to make inferences about the time point a new case is currently at – and, therefore, indicate how long it is before an outcome event is likely to occur.
Clearly, there are more developments to be made to the Indicator Waves method, and further opportunities to expand the method to analyse wider ranges of data and cases. Already, the Researchers in Behaviour Sequence Analysis (ReBSA) are developing approaches to further clarify the case matching analyses, as well as working on experimental analyses to show the reliability of datasets. This presentation will provide attendees with an overview of the Indicator Waves approach, and highlight some of these further analyses that are currently being developed.
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