From pre-processing to advanced dynamic modeling of pupil data.

The pupil of the eye provides a rich source of information for cognitive scientists, as it can index a variety of bodily states (e.g., arousal, fatigue) and cognitive processes (e.g., attention, decision-making). As pupillometry becomes a more accessible and popular methodology, researchers have proposed a variety of techniques for analyzing pupil data. Here, we focus on time series-based, signal-to-signal approaches that enable one to relate dynamic changes in pupil size over time with dynamic changes in a stimulus time series, continuous behavioral outcome measures, or other participants' pupil traces. We first introduce pupillometry, its neural underpinnings, and the relation between pupil measurements and other oculomotor behaviors (e.g., blinks, saccades), to stress the importance of understanding what is being measured and what can be inferred from changes in pupillary activity. Next, we discuss possible pre-processing steps, and the contexts in which they may be necessary. Finally, we turn to signal-to-signal analytic techniques, including regression-based approaches, dynamic time-warping, phase clustering, detrended fluctuation analysis, and recurrence quantification analysis. Assumptions of these techniques, and examples of the scientific questions each can address, are outlined, with references to key papers and software packages. Additionally, we provide a detailed code tutorial that steps through the key examples and figures in this paper. Ultimately, we contend that the insights gained from pupillometry are constrained by the analysis techniques used, and that signal-to-signal approaches offer a means to generate novel scientific insights by taking into account understudied spectro-temporal relationships between the pupil signal and other signals of interest.