Proportional hazards modeling of saccadic response times during reading

In this article we use proportional hazards models to examine how low-level processes affect the probability of making a saccade over time, through the period of fixation, during reading. We apply the Cox proportional hazards model to investigate how launch distance (relative to word beginning), fixation location (relative to word center), and word frequency affect the hazard of a saccadic response. This model requires that covariates have a constant impact on the hazard over time, the assumption of proportional hazards. We show that this assumption is not supported. The impact of the covariates changes with the time passed since fixation onset. To account for the non-proportional hazards we fit step functions of time, resulting in a model with time-varying effects on the hazard. We evaluate the ability to predict the timing of saccades on held-out fixation data. The model with time-varying effects performs better in predicting the timing of saccades for fixations as short as 100 ms and as long as 500 ms, when compared both to a baseline model without covariates and a model which assumes constant covariate effects. This result suggests that the time-varying effects model better recovers the time course of low-level processes that influence the decision to move the eyes.