Revealing the time course of signals influencing the generation of secondary saccades using Aalen's additive hazards model

- Additive hazard models reveal time-dependent influences on secondary saccades.
- Error-correcting and error-unrelated signals influence secondary saccade generation.
- We evaluate a qualitative model for secondary (micro-)saccade generation.

Saccadic eye movements are frequently followed by smaller secondary saccades which are generally assumed to correct for the error in primary saccade landing position. However, secondary saccades can also occur after accurate primary saccades and they are often as small as microsaccades, therefore raising the need to further scrutinize the processes involved in secondary saccade generation. Following up a previous study, we analyzed secondary saccades using rate analysis which allows us to quantify experimental effects as shifts in distributions, therefore going beyond comparisons of mean differences. We use Aalen's additive hazards model to delineate the time course of key influences on the secondary saccade rate. In addition to the established effect of primary saccade error, we observed a time-varying influence of under- vs. overshooting - with a higher risk of generating secondary saccades following undershoots. Moreover, increasing target eccentricity influenced the programming of secondary saccades, therefore demonstrating that error-unrelated variables co-determine secondary saccade programs. Our results provide new insights into the generative mechanisms of small saccades during postsaccadic fixation that need to be accounted for by secondary saccade models.