Analyzing the Time Course of Pupillometric Data

This article provides a tutorial for analyzing pupillometric data. Pupil dilation has become increasingly popular in psychological and psycholinguistic research as a measure to trace language processing. However, there is no general consensus about procedures to analyze the data, with most studies analyzing extracted features from the pupil dilation data instead of analyzing the pupil dilation trajectories directly. Recent studies have started to apply nonlinear regression and other methods to analyze the pupil dilation trajectories directly, utilizing all available information in the continuously measured signal. This article applies a nonlinear regression analysis, generalized additive mixed modeling, and illustrates how to analyze the full-time course of the pupil dilation signal. The regression analysis is particularly suited for analyzing pupil dilation in the fields of psychological and psycholinguistic research because generalized additive mixed models can include complex nonlinear interactions for investigating the effects of properties of stimuli (e.g., formant frequency) or participants (e.g., working memory score) on the pupil dilation signal. To account for the variation due to participants and items, nonlinear random effects can be included. However, one of the challenges for analyzing time series data is dealing with the autocorrelation in the residuals, which is rather extreme for the pupillary signal. On the basis of simulations, we explain potential causes of this extreme autocorrelation, and on the basis of the experimental data, we show how to reduce their adverse effects, allowing a much more coherent interpretation of pupillary data than possible with feature-based techniques.