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Related Concept Videos

Residual Plots01:07

Residual Plots

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A residual plot is a statistical representation of data used to analyze correlation and regression results. It helps verify the requirements for drawing specific conclusions about correlation and regression. To obtain the residual plot, first, the residual for each data value is calculated, which is simply the vertical distance between the observed and the predicted value obtained from the regression equation.
When the residual values are plotted against the variable x, it is called a residual...
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Residual Stresses01:26

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Residual stresses reside in a structure even after removing the original stress inducer. This phenomenon often arises from varied plastic deformations across different parts of a structure. Consider a rod stretched beyond its yield point. It will not regain its original length due to permanent deformation. Even after load removal, the rod does not entirely lose stress because of uneven plastic deformations, resulting in residual stresses. The computation of these stresses in structures is...
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Residual Stresses in Circular Shafts01:10

Residual Stresses in Circular Shafts

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In materials that exhibit elastic and plastic behavior, known as elastoplastic materials, residual stresses can accumulate when these materials experience plastic deformation. This deformation arises from either high levels of shearing stress or significant strains. Residual stresses are internal stresses that persist within a material after removing the external force causing deformation. This phenomenon is demonstrated when observing the behavior of a shaft under torque; notably, the...
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Residual Stresses in Bending01:18

Residual Stresses in Bending

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In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...
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Residuals and Least-Squares Property01:11

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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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Albert Bandura's theory of observational learning identifies four critical processes: attention, retention, motor reproduction, and reinforcement or motivation.
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Model-Based Residual Post-Processing for Residual Model Identification.

Moustafa M A Ibrahim1,2, Rikard Nordgren1, Maria C Kjellsson1

  • 1Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden.

The AAPS Journal
|July 4, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces a model-based diagnostic tool using conditional weighted residuals (CWRES) to identify and fix model errors in residual unexplained variability (RUV) models. CWRES effectively predicts model misspecifications and improvement in fit, offering a fast, automated solution for RUV model development.

Keywords:
conditional weighted residualsdiagnosticsmodel evaluationnonlinear mixed effects modelsresidual error model

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Area of Science:

  • Pharmacometrics
  • Computational Statistics
  • Model Development and Evaluation

Background:

  • Model misspecification is a common challenge in pharmacokinetic/pharmacodynamic (PK/PD) modeling.
  • Residual unexplained variability (RUV) models are crucial for describing unexplained variability.
  • Existing diagnostics may not always quantitatively identify specific model deficiencies or guide model improvement effectively.

Purpose of the Study:

  • To evaluate model-based post-processing of diagnostics, specifically conditional weighted residuals (CWRES), as a tool for quantitatively identifying model misspecifications.
  • To assess the utility of CWRES in guiding rectifying actions for residual unexplained variability (RUV) models.
  • To determine if CWRES can rapidly and robustly predict the necessity and impact of extending RUV models.

Main Methods:

  • Investigated CWRES as a primary diagnostic tool for model misspecification.
  • Applied CWRES to scan and evaluate extended RUV models, including autocorrelated errors, dynamic transform both sides, inter-individual variability on RUV, power error model, t-distributed errors, and time-varying error magnitude.
  • Compared the predictive performance of CWRES against other diagnostics (CWRESI, IWRES, NPDE) using real and simulated data, focusing on goodness-of-fit improvements (ΔOFV).

Main Results:

  • CWRES modeling accurately predicted the nature of model misspecifications, the magnitude of expected improvement in fit (ΔOFV), and relevant parameter estimates for model extensions.
  • Extended RUV models evaluated using CWRES demonstrated superior data description capabilities.
  • CWRES exhibited higher predictive performance for ΔOFV compared to alternative metrics like CWRESI, IWRES, and NPDE.

Conclusions:

  • Model-based post-processing with CWRES serves as a fast, automated, and effective diagnostic tool for RUV model development and evaluation.
  • CWRES quantitatively identifies model misspecifications and guides rectifying actions, improving model descriptions.
  • The methodology is already implemented in the PsN software package, facilitating its practical application.