从密集的纵向数据中解锁非线性动态和多稳定性:一种新的方法方法
Jingmeng Cui1, Fred Hasselman2, Anna Lichtwarck-Aschoff1
1Faculty of Behavioural and Social Sciences, University of Groningen.
Psychological methods
|December 14, 2023
概括
一个新的R包,fitlandr,从密集的纵向数据 (ILD) 中分析复杂的心理动态. 它区分了真正的可比性和纯粹的双模性,为非线性系统分析提供了强大的工具.
科学领域:
- 心理学 心理学 心理学
- 计算社会科学 计算社会科学
- 数据科学数据科学数据科学
背景情况:
- 智能设备可以进行密集的纵向数据 (ILD) 收集,这对于理解心理动态至关重要.
- 传统的时间序列方法与心理系统固有的非线性复杂性作斗争.
- 限制包括线性假设和受限制的模型形式.
研究的目的:
- 介绍fitlandr,一个R包用于分析ILD复杂的心理动态.
- 整合漂移-扩散函数和稳定性景观的非参数估计.
- 解决现有的时间序列方法在捕捉非线性系统行为的局限性.
主要方法:
- 使用多变量内核估计器 (MVKE) 进行非参数漂移-扩散函数估计.
- 使用稳定态分布的蒙特卡洛估计,用于稳定性景观分析.
- 实现fitlandr作为一个R包用于实际应用.
主要成果:
- 菲特兰德成功地从模拟的情绪系统中恢复了可视化的动态,即使有噪音.
- 该方法优先考虑动态信息,而不是分布信息,以便进行准确的分析.
- 应用于实证ILD,Fitlandr在一个数据集中确定了可比性,尽管两者都显示双模性,突出了区别.
结论:
- 在ILD中,fitlandr有效地区分了真正的可比性和仅仅是数据双方式.
- R包为揭示心理系统中的非线性动态提供了一个强大的工具.
- 展示了动态信息对于准确的心理系统分析的重要性.
相关概念视频
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
56
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
56
Mechanistic Models: Compartment Models in Individual and Population Analysis
43
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
43
Linear Approximation in Time Domain
83
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
83
Linear Approximation in Frequency Domain
91
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
91
Multimachine Stability
163
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
163
Introduction To Survival Analysis
243
Survival analysis is a statistical method used to study time-to-event data, where the "event" might represent outcomes like death, disease relapse, system failure, or recovery. A unique feature of survival data is censoring, which occurs when the event of interest has not been observed for some individuals during the study period. This requires specialized techniques to handle incomplete data effectively.
The primary goal of survival analysis is to estimate survival time—the time...
The primary goal of survival analysis is to estimate survival time—the time...
243


