Variance and Distribution Models for Steering Tasks.
Variance and Distribution Models for Steering Tasks.
复制标题
DOI：
10.1145/3472749.3474811
复制
发表时间：
2021-10
期刊：
影响因子：
--
通讯作者：
Bi X
中科院分区：
文献类型：
--
作者：
Wang M;Zhao H;Zhou X;Ren X;Bi X
转向定律揭示了基于轨迹的转向任务中运动时间（MT）和难度指数（ID）之间的线性关系。然而，它并不将 MT 的方差或分布与 ID 联系起来。在本文中，我们提出并评估了基于 ID 的转向任务预测 MT 方差和分布的模型。我们首先提出了一个二次方差模型，它揭示了 MT 的方差与 ID 呈二次相关，线性系数为 0。对新数据集和之前收集的数据集的经验评估表明，二次方差模型占观察到的 MT 方差的 78% 到 97% 之间；它优于其他候选模型，例如线性模型和常数模型；添加线性系数不会导致模型适应性的改善。方差模型可以预测给定 ID 的 MT 分布：我们可以使用方差模型来预测方差（或尺度）参数，使用 Steering law 来预测分布的平均值（或位置）参数。我们评估了六种类型的分布来预测 MT 的分布。我们的研究还表明，在预测 MT 分布时，正偏态分布（例如 Gamma、对数正态、指数修正高斯分布 (ExGaussian) 和极值分布）优于对称分布（例如高斯分布和截断高斯分布），并且 Gamma 分布的表现略好于其他正偏态分布。总体而言，我们的研究将转向任务的 MT 预测从点估计推进到方差和分布估计，这提供了对转向行为的更完整的理解，并量化了 MT 预测的不确定性。
Steering law reveals a linear relationship between the movement time (MT) and the index of difficulty (ID) in trajectory-based steering tasks. However, it does not relate the variance or distribution of MT to ID. In this paper, we propose and evaluate models that predict the variance and distribution of MT based on ID for steering tasks. We first propose a quadratic variance model which reveals that the variance of MT is quadratically related to ID with the linear coefficient being 0. Empirical evaluation on a new and a previously collected dataset show that the quadratic variance model accounts for between 78% and 97% of variance of observed MT variances; it outperforms other model candidates such as linear and constant models; adding the linear coefficient leads to no improvement on the model fitness. The variance model enables predicting the distribution of MT given ID: we can use the variance model to predict the variance (or scale) parameter and Steering law to predict the mean (or location) parameter of a distribution. We have evaluated six types of distributions for predicting the distribution of MT. Our investigation also shows that positively skewed distribution such as Gamma, Lognormal, Exponentially Modified Gaussian (ExGaussian), and Extreme value distributions outperformed the symmetric distribution such as Gaussian and truncated Gaussian distribution in predicting the MT distribution, and Gamma distribution performed slightly better than other positively skewed distributions. Overall, our research advances the MT prediction of steering tasks from a point estimate to variance and distribution estimates, which provides a more complete understanding of steering behavior and quantifies the uncertainty of MT prediction.