Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures from...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

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)...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Spatially Correlated Analysis of Infectious Disease Outcomes Based on Bayesian Functional Hierarchical Models.

Statistics in medicine·2026
Same author

Signal-to-Noise Ratio in Estimating and Testing the Mediation Effect: Structural Equation Modeling versus Path Analysis with Weighted Composites.

Psychometrika·2026
Same author

Functional varying-coefficient Cox model and its application.

Statistical methods in medical research·2026
Same author

Servant Leadership in Higher Education: A Graded Response Model Approach to Item Response Theory Analysis.

Psychological reports·2025
Same author

The Improved EMS Algorithm for Latent Variable Selection in M3PL Model.

Applied psychological measurement·2024
Same author

Signal-to-Noise Ratio in Estimating and Testing the Mediation Effect: Structural Equation Modeling versus Path Analysis with Weighted Composites.

Psychometrika·2024
Same journal

A Kurtosis-Adjusted Bias Correction for the Standardized Mean Difference: Extending Hedges' <i>g</i> to Nonnormal Populations.

Educational and psychological measurement·2026
Same journal

A Simple Approach for Differential Test Functioning Based on Sum Scores.

Educational and psychological measurement·2026
Same journal

Evaluating Factor Retention in Large Factor Analysis Models: A Simulation Study Comparing 15 Methods.

Educational and psychological measurement·2026
Same journal

Agreement and Alignment in Binary Rating Tasks: Strategic Convergence as an Equilibrium Outcome.

Educational and psychological measurement·2026
Same journal

Interactions Between Termination Criteria and Ability Estimators in Computerized Adaptive Testing.

Educational and psychological measurement·2026
Same journal

Identification and Diagnosis of Misreporting in Surveys.

Educational and psychological measurement·2026
See all related articles

Related Experiment Video

Updated: Jun 2, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

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

Published on: July 3, 2020

Constrained Maximum Likelihood Estimation for Two-level Mean and Covariance Structure Models.

Peter M Bentler1, Jiajuan Liang, Man-Lai Tang

  • 1University of California, Los Angeles.

Educational and Psychological Measurement
|May 6, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces an EM-type algorithm for estimating structural equation model parameters with linear and nonlinear constraints. The new method efficiently handles complex constraints in two-level models, validated by simulation and real-world data.

More Related Videos

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits
08:27

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits

Published on: September 27, 2019

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
06:52

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Published on: September 17, 2019

Related Experiment Videos

Last Updated: Jun 2, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

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

Published on: July 3, 2020

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits
08:27

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits

Published on: September 27, 2019

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
06:52

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Published on: September 17, 2019

Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Maximum likelihood estimation is standard for two-level structural equation models.
  • Handling parameter constraints, especially nonlinear ones, poses challenges in standard analyses.
  • Existing methods may struggle with complex constraint scenarios in hierarchical data.

Purpose of the Study:

  • To develop an EM-type algorithm for parameter estimation in two-level structural equation models.
  • To accommodate both linear and nonlinear constraints on model parameters.
  • To provide a flexible and robust estimation method for complex hierarchical models.

Main Methods:

  • Development of an expectation-maximization (EM)-type algorithm.
  • Incorporation of linear and nonlinear constraints within the estimation framework.
  • Validation through a Monte Carlo simulation study.
  • Application to a real two-level dataset using a mean and covariance structure model.

Main Results:

  • The proposed EM-type algorithm effectively estimates model parameters under both linear and nonlinear constraints.
  • Monte Carlo simulations demonstrate the empirical performance and stability of the algorithm.
  • The algorithm successfully handles complex constraint scenarios in two-level models.

Conclusions:

  • The developed EM-type algorithm offers a powerful tool for structural equation modeling with parameter constraints.
  • This method enhances the analysis of complex hierarchical data structures.
  • It provides a practical solution for researchers facing constrained estimation problems.