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Assessing and tracking physiological and cognitive states of multiple individuals interacting in virtual environments is of increasing interest to the virtual reality (VR) community. In this paper, we describe a team-based VR task termed the Apollo Distributed Control Task (ADCT), where individuals, via the single independent degree-of-freedom control and limited environmental views, must work together to guide a virtual spacecraft back to Earth. Novel to the experiment is that 1) we simultaneously collect multiple physiological measures including electroencephalography (EEG), pupillometry, speech signals, and individual's actions, 2) we regulate the the difficulty of the task and the type of communication between the teammates. Focusing on the analysis of pupil dynamics, which have been linked to a number of cognitive and physiological processes such as arousal, cognitive control, and working memory, we find that pupil diameter changes are predictive of multiple task-related dimensions, including the difficulty of the task, the role of the team member, and the type of communication. 

Summary Large samples are generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyse such large samples because of high computational costs. In particular, the daunting computational cost of selecting smoothing parameters renders smoothing spline ANOVA models impractical. In this article, we develop an asympirical, i.e., asymptotic and empirical, smoothing parameters selection method for smoothing spline ANOVA models in large samples. The idea of our approach is to use asymptotic analysis to show that the optimal smoothing parameter is a polynomial function of the sample size and an unknown constant. The unknown constant is then estimated through empirical subsample extrapolation. The proposed method significantly reduces the computational burden of selecting smoothing parameters in high-dimensional and large samples. We show that smoothing parameters chosen by the proposed method tend to the optimal smoothing parameters that minimize a specific risk function. In addition, the estimator based on the proposed smoothing parameters achieves the optimal convergence rate. Extensive simulation studies demonstrate the numerical advantage of the proposed method over competing methods in terms of relative efficacy and running time. In an application to molecular dynamics data containing nearly one million observations, the proposed method has the best prediction performance.