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Stability of structures01:14

Stability of structures

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In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
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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...
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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.
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Stability01:28

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The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
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Pole and System Stability01:24

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The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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Regularized structural equation modeling with stability selection.

Xiaobei Li1, Ross Jacobucci1

  • 1Department of Psychology, University of Notre Dame.

Psychological Methods
|January 28, 2021
PubMed
Summary
This summary is machine-generated.

Stability selection enhances regularized structural equation modeling (SEM) by reducing false positives, improving coefficient selection in high-dimensional data. This method overcomes limitations of the least absolute shrinkage and selection operator (LASSO) for social and behavioral research.

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Area of Science:

  • Statistics
  • Social and Behavioral Sciences
  • Psychometrics

Background:

  • Regularization methods like LASSO are used for high-dimensional data.
  • Regularized SEM aims to apply regularization benefits to social/behavioral models.
  • LASSO in SEM can suffer from high false positive rates and inconsistent selection.

Purpose of the Study:

  • To introduce and evaluate stability selection for regularized SEM.
  • To address limitations of LASSO in regularized SEM, specifically false positives and selection instability.
  • To improve coefficient selection in high-dimensional SEM using stability selection.

Main Methods:

  • Application of stability selection to regularized SEM.
  • Utilizing repeated data resampling to identify stable coefficients.
  • Conducting two simulation studies to compare stability selection with LASSO.

Main Results:

  • Stability selection significantly improves upon LASSO in selecting correct paths.
  • Stability selection effectively reduces the number of false positives in regularized SEM.
  • Demonstrated application in two empirical examples.

Conclusions:

  • Stability selection is a valuable mechanism for enhancing regularized SEM.
  • The method overcomes key limitations of LASSO, leading to more reliable model estimation.
  • Future research directions for stability selection in SEM are discussed.