Constrained Multivariate Functional Principal Components Analysis for Novel Outcomes in Eye-Tracking Experiments

Individuals with autism spectrum disorder (ASD) tend to experience greater difficulties with social communication and sensory information processing. Of particular interest in ASD biomarker research is the study of visual attention, effectively quantified in eye tracking (ET) experiments. Eye tracking offers a powerful, safe, and feasible platform for gaining insights into attentional processes by measuring moment-by-moment gaze patterns in response to stimuli. Even though recording is done with millisecond granularity, analyses commonly collapse data across trials into variables such as proportion time spent looking at a region of interest (ROI). In addition, looking times in different ROIs are typically analyzed separately. We propose a novel multivariate functional outcome that carries proportion looking time information from multiple regions of interest jointly as a function of trial type, along with a novel constrained multivariate functional principal components analysis procedure to capture the variation in this outcome. The method incorporates the natural constraint that the proportion looking times from the multiple regions of interest must sum up to one. Our approach is motivated by the Activity Monitoring task, a social-attentional assay within the ET battery of the Autism Biomarkers Consortium for Clinical Trials (ABC-CT). Application of our methods to the ABC-CT data yields new insights into dominant modes of variation of proportion looking times from multiple regions of interest for school-age children with ASD and their typically developing (TD) peers, as well as richer analysis of diagnostic group differences in social attention.