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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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An Inverse-Linear Logistic Model of The Main Sequence.

Andrew T Duchowski¹, Krzysztof Krejtz², Cezary Biele³

¹Clemson University Clemson, SC, USA.

Journal of Eye Movement Research

|April 8, 2021

Summary

A novel logistic function model accurately describes eye movement characteristics like velocity and amplitude. This robust model fits small and mid-amplitude data, with potential for large-amplitude movements.

Keywords:

main sequence microsaccades non-linear modeling saccades

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Area of Science:

Ophthalmology
Neuroscience
Biophysics

Background:

Understanding eye movement dynamics is crucial for diagnosing neurological and visual disorders.
Existing models often struggle to capture the full range of eye movement characteristics.

Purpose of the Study:

To introduce a new mathematical model for eye movements based on the logistic function.
To demonstrate the model's ability to accurately represent the peak velocity-amplitude and duration-amplitude relationships.

Main Methods:

Developed an inverse-linear logistic model.
Fitted the model to aggregate data including microsaccades, saccades, and their superposition.
Assessed the model's fit across small and mid-amplitude ranges.

Main Results:

The logistic model exhibits an S-curve fit to the peak velocity-amplitude relation.
The model effectively controls curve asymptotes and slope in the mid-amplitude range.
The model accurately expresses the linear duration-amplitude relationship.

Conclusions:

The proposed logistic model offers a robust and flexible approach to characterizing eye movements.
The model's utility is demonstrated for small and mid-amplitude eye movements.
The model is expected to extend effectively to large-amplitude eye movements.