Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Factorial Design

Factorial Design

Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level. One way to test this hypothesis is by categorizing salary into three levels (low, moderate, and high) and skills sets into two levels (entry level...

Confidence Interval for Estimating Population Mean

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...

The Nernst Equation

The Nernst Equation

Nonstandard Reaction Conditions
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy change ΔG° and equilibrium constant K has been previously explored. For example, a redox reaction involving zinc(II) and tin(II) ions at 1 M concentration with Eºcell = +0.291 V and ΔG° = −56.2 kJ is spontaneous.

Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.

Modeling with Differential Equations

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

Chemical Equations

Chemical Equations

Chemical equations represent the identities and relative quantities of substances involved in a chemical reaction. The substances undergoing reaction are called reactants, and their formulas are placed on the left side of the equation. The substances generated by the reaction are called products, and their formulas are placed on the right side of the equation. Plus signs (+) separate individual reactant and product formulas, and an arrow (→) separates the reactant and product (left and right)...

You might also read

Related Articles

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

Sort by

Same author

Cumulant-Based Approaches for Testing the Assumption of Independent Errors in Non-Gaussian Parallel and Congeneric Measures.

Educational and psychological measurement·2026

Same author

Leveraging computerized adaptive testing for cost-effective evaluation of large language models in medical benchmarking.

NPJ digital medicine·2026

Same author

Indirect Effects of the Coping Power Intervention on Latent Suicidal Thoughts and Behaviors: an Integrative Data Analysis.

Prevention science : the official journal of the Society for Prevention Research·2026

Same author

Does X at Time 1 Cause Y at Time 2? Longitudinal Causal Learning with Hidden Confounders.

Psychometrika·2026

Same author

Fine-grained evaluation of large language models in medicine using non-parametric cognitive diagnostic modeling.

Scientific reports·2026

Same author

Empowering Expert Judgment: A Data-Driven Decision Framework for Standard Setting in High-Dimensional and Data-Scarce Assessments.

Educational and psychological measurement·2026

Same journal

Bayesian Machine Learning Tools for Alcohol Use Disorder Research: The bpaup R Package.

Multivariate behavioral research·2026

Same journal

A Unified Framework for Jointly modelling Response Times and Item Position Effects in Computer-Based Learning Assessments.

Multivariate behavioral research·2026

Same journal

Generalizability Theory Applied to Daily Relationship Quality: Substantive and Statistical Directions.

Multivariate behavioral research·2026

Same journal

A Modularized Higher-Order Diagnostic Classification Model for Clustered Attribute Hierarchies.

Multivariate behavioral research·2026

Same journal

Generalizing Causal Effects to a Target Population Without Individual-Level Data from the Target Population.

Multivariate behavioral research·2026

Same journal

betaselectr: Selective (and Proper) Standardization in Structural Equation Models.

Multivariate behavioral research·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jan 31, 2026

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

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

Published on: July 3, 2020

Evaluating Factorial Invariance: An Interval Estimation Approach Using Bayesian Structural Equation Modeling.

Dexin Shi¹, Hairong Song², Christine DiStefano¹

¹a University of South Carolina.

Multivariate Behavioral Research

|December 21, 2018

Summary

This summary is machine-generated.

This study presents a Bayesian approach for evaluating factorial invariance using highest density intervals (HDI) and a region of practical equivalence (ROPE). This method offers more informative conclusions than traditional tests for assessing measurement invariance.

Keywords:

Bayesian SEM factorial invariance highest density interval parameter estimation region of practical equivalence

More Related Videos

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Published on: April 25, 2025

Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations

Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations

Published on: January 8, 2013

Related Experiment Videos

Last Updated: Jan 31, 2026

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

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

Published on: July 3, 2020

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure

Published on: April 25, 2025

Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations

Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations

Published on: January 8, 2013

Area of Science:

Psychometrics
Statistical modeling
Structural equation modeling

Background:

Factorial invariance is crucial for comparing latent constructs across groups.
Traditional methods like likelihood ratio tests have limitations in assessing practical significance.
Bayesian approaches offer a framework for incorporating uncertainty and practical equivalence.

Purpose of the Study:

To introduce an interval estimation approach for evaluating factorial invariance using Bayesian structural equation modeling.
To provide researchers with a method to assess the practical importance of parameter noninvariance.
To offer a more informative alternative to traditional factorial invariance testing.

Main Methods:

Utilizing Bayesian parameter estimation to assess noninvariance with highest density intervals (HDI).
Comparing 95% HDI with a region of practical equivalence (ROPE) to evaluate invariance.
Applying structural equation modeling within a Bayesian framework.

Main Results:

The proposed Bayesian approach provides additional insights beyond traditional likelihood ratio tests.
Researchers can support the null hypothesis of practical invariance.
The method allows for the examination of the practical importance of noninvariant parameters.

Conclusions:

The Bayesian interval estimation approach enhances the evaluation of factorial invariance.
This method leads to more informative conclusions in applied research.
The choice of ROPE significantly influences the interpretation of results.