An inverse-linear logistic model of the main sequence

Abstract

A model of the main sequence is proposed based on the logistic function. The model’s fit to the peak velocity-amplitude relation resembles an S curve, simulta- neously allowing control of the curve’s asymptotes at very small and very large amplitudes, as well as its slope over the mid amplitude range. The proposed inverse-linear logistic model is also able to express the linear relation of duration and amplitude. We demonstrate the utility and robustness of the model when fit to aggregate data at the small- and mid-amplitude ranges, namely when fitting microsaccades, saccades, and superposition of both. We are confident the model will suitably extend to the large-amplitude range of eye movements.

Keywords

• saccades
• microsaccades
• main sequence
• non-linear modeling