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

Odds Ratio01:09

Odds Ratio

2.1K
The odds ratio (OR) is a statistical measure used extensively in epidemiology and research to quantify the strength of association between exposure and outcome across different groups. Unlike relative risk, which compares the probabilities of an event occurring, the odds ratio compares the odds of an event occurring in the exposed group to the odds of it occurring in the unexposed group. The odds, in this context, are calculated as the probability of the event happening divided by the...
2.1K
Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

535
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...
535
Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

8.8K
A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).
8.8K
Spearman's Rank Correlation Test01:20

Spearman's Rank Correlation Test

1.6K
Spearman's rank correlation test, also known as Spearman's rho, is a nonparametric method for assessing the strength and direction of association between two variables. This test is particularly valuable when the data distribution is unknown or when the assumption of normality does not hold. Named after the English psychologist and statistician Dr. Charles Edward Spearman, it serves as the nonparametric counterpart to Pearson's correlation coefficient.
Spearman's test calculates correlation by...
1.6K
Goodness-of-Fit Test01:16

Goodness-of-Fit Test

9.4K
The goodness-of-fit test is a type of hypothesis test which determines whether the data "fits" a particular distribution. For example, one may suspect that some anonymous data may fit a binomial distribution. A chi-square test (meaning the distribution for the hypothesis test is chi-square) can be used to determine if there is a fit. The null and alternative hypotheses may be written in sentences or stated as equations or inequalities. The test statistic for a goodness-of-fit test is given as...
9.4K
Ranks01:02

Ranks

563
Unlike parametric methods, nonparametric statistics are ideal for nominal and ordinal data, requiring fewer assumptions about the population's nature or distribution. This makes nonparametric methods easier to apply and interpret, as they do not depend on parameters like mean or standard deviation. One common approach in nonparametric analysis is to sort data according to a specific criterion. For instance, we might arrange weather data from hottest to coldest days in a month or rank cities...
563

You might also read

Related Articles

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

Sort by
Same author

DIF Analysis with Unknown Groups and Anchor Items.

Psychometrika·2026
Same author

Maximum Softly Penalized Likelihood in Factor Analysis.

Psychometrika·2026
Same author

Unfolding the Network of Peer Grades: A Latent Variable Approach.

Psychometrika·2025
Same author

The generalized Hausman test for detecting non-normality in the latent variable distribution of the two-parameter IRT model.

The British journal of mathematical and statistical psychology·2024
Same author

Pairwise likelihood estimation and limited-information goodness-of-fit test statistics for binary factor analysis models under complex survey sampling.

The British journal of mathematical and statistical psychology·2024
Same author

Pairwise stochastic approximation for confirmatory factor analysis of categorical data.

The British journal of mathematical and statistical psychology·2024

Related Experiment Video

Updated: Mar 13, 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

3.8K

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables.

Myrsini Katsikatsou1, Irini Moustaki2

  • 1Department of Statistics, London School of Economics, Houghton Street, London, WC2A 2AE , UK. m.katsikatsou@lse.ac.uk.

Psychometrika
|October 14, 2016
PubMed
Summary

This study introduces new likelihood ratio test statistics for structural equation models with correlated ordinal data. These methods, implemented in R, offer a flexible framework for model fitting and testing, showing satisfactory performance in simulations.

Keywords:
composite likelihoodlatent variable modellingunderlying variable approach

More Related Videos

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

3.0K
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

7.3K

Related Experiment Videos

Last Updated: Mar 13, 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

3.8K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

3.0K
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

7.3K

Area of Science:

  • Statistics
  • Econometrics
  • Psychometrics

Background:

  • Correlated multivariate ordinal data analysis often employs structural equation models (SEMs).
  • Limited-information methods like three-stage least squares and pairwise maximum likelihood estimation (PMLE) are common for parameter estimation.
  • Existing methods for model fit testing in this context have limitations.

Purpose of the Study:

  • To derive and evaluate likelihood ratio test statistics for overall goodness-of-fit and nested models within the PMLE framework for SEMs with ordinal data.
  • To assess the performance of these new statistics through simulations.
  • To provide model selection criteria (AIC, BIC) compatible with the PMLE framework.

Main Methods:

  • Derivation of two likelihood ratio test statistics and their asymptotic distributions under PMLE.
  • Monte Carlo simulations to evaluate type I error rates and statistical power.
  • Application of derived statistics and model selection criteria to real-world survey data ('trust in the police').
  • Implementation in the R package lavaan.

Main Results:

  • The proposed likelihood ratio test statistics demonstrate satisfactory performance regarding type I error and power in simulations.
  • Their performance is comparable to statistics derived under three-stage least squares methods.
  • The derived AIC and BIC criteria effectively select the correct model in simulation examples.
  • The methods were successfully applied to analyze 'trust in the police' data.

Conclusions:

  • The derived likelihood ratio test statistics and model selection criteria offer a flexible and effective framework for fitting and testing SEMs with ordinal data using PMLE.
  • These tools enhance the analysis of complex correlated ordinal data.
  • The R package lavaan now includes these advanced statistical methods for broader accessibility.