A Novel Mixture Model for Characterizing Human Aiming Performance Data

TL;DR

This paper introduces a new mixture model combining Gaussian and exponential components to better characterize human aiming performance data, especially in real-world scenarios where data show skewness, and demonstrates its effectiveness through simulations and empirical analysis.

Contribution

A novel two-component mixture model with an ECM algorithm for estimating human aiming data, capturing skewness and non-minimization regions more effectively than existing models.

Findings

Model accurately captures skewed aiming data.

Effective in identifying non-minimization regions.

Demonstrated through extensive simulations and real data analysis.

Abstract

Fitts' law is often employed as a predictive model for human movement, especially in the field of human-computer interaction. Models with an assumed Gaussian error structure are usually adequate when applied to data collected from controlled studies. However, observational data (often referred to as data gathered "in the wild") typically display noticeable positive skewness relative to a mean trend as users do not routinely try to minimize their task completion time. As such, the exponentially-modified Gaussian (EMG) regression model has been applied to aimed movements data. However, it is also of interest to reasonably characterize those regions where a user likely was not trying to minimize their task completion time. In this paper, we propose a novel model with a two-component mixture structure -- one Gaussian and one exponential -- on the errors to identify such a region. An expectation-conditional-maximization (ECM) algorithm is developed for estimation of such a model and some properties of the algorithm are established. The efficacy of the proposed model, as well as its ability to inform model-based clustering, are addressed in this work through extensive simulations and an insightful analysis of a human aiming performance study.