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Related Concept Videos

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
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Mechanistic Models: Compartment Models in Individual and Population Analysis

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 squares (OLS)...
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Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
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Related Experiment Video

Updated: Jun 12, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Published on: July 3, 2020

A semiparametric Bayesian approach for structural equation models.

Xin-Yuan Song1, Jun-Hao Pan, Timothy Kwok

  • 1Department of Statistics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong. xysong@sta.cuhk.edu.hk <xysong@sta.cuhk.edu.hk>

Biometrical Journal. Biometrische Zeitschrift
|June 10, 2010
PubMed
Summary

Structural equation models (SEMs) often violate normality assumptions. This study shows that modeling residuals nonparametrically while assuming latent variable normality is a reliable approach for SEMs with non-normal data.

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Last Updated: Jun 12, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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08:27

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Published on: September 27, 2019

Area of Science:

  • Statistics
  • Econometrics
  • Psychometrics

Background:

  • Structural Equation Models (SEMs) typically assume normally distributed observed variables.
  • Non-normality in SEMs can arise from latent variables, residuals, or both.
  • Violated normality assumptions can significantly impact model estimation and interpretation.

Purpose of the Study:

  • To investigate the identifiability and estimation challenges in SEMs with non-normal latent variables and residuals.
  • To propose a semiparametric Bayesian approach for handling non-normality in SEMs.
  • To provide practical recommendations for SEM model development when normality assumptions are violated.

Main Methods:

  • Identifiability analysis of SEMs with unknown latent variable and residual distributions.
  • Development of a semiparametric Bayesian method using a truncated Dirichlet process with a stick-breaking prior.
  • Simulation studies and real data analysis to evaluate the proposed methodology.

Main Results:

  • SEMs are nonidentifiable when both latent variable and residual distributions are unknown.
  • Residual non-normality in the measurement equation has a more severe impact on parameter estimation than latent variable non-normality.
  • The proposed semiparametric Bayesian approach effectively handles residual non-normality.

Conclusions:

  • Parametric assumptions are necessary for reliable estimation when distributions are unknown.
  • Prioritizing nonparametric modeling of residuals over latent variables is recommended when distribution information is lacking.
  • The developed semiparametric Bayesian method offers a robust solution for SEMs with non-normal residuals.