Normal Versus Noncentral Chi-square Asymptotics of Misspecified Models
Bibliographic Data
| ID | 19290106 |
|---|---|
| Authors | So Yeon Chun (0000-0002-2836-0302, Georgia Institute of Technology), Alexander Shapiro (0000-0002-6624-2091, Georgia Institute of Technology) |
| Year | 2009 |
| Volume | 44 |
| Issue | 6 |
| Pages | 803-827 |
| Publication date | 2009-11-30 |
| Open Access | No |
| Type | ARTICLE |
| Venue | Multivariate Behavioral Research (JOURNAL) |
| Journal identifiers | ISSN: 0027-3171 • E-ISSN: 1532-7906 |
| Publisher | Informa UK Limited (PUBLISHER • GB) |
| DOI | 10.1080/00273170903352186 |
| PMID | 26801797 |
| OpenAlex | W2119082688 |
| Language | EN |
| Citations received | 5 |
| References cited | 18 |
The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equation modeling. Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main goal of this article is to evaluate the validity of employing these distributions in practice. Monte Carlo simulation results indicate that the noncentral chi-square distribution describes behavior of the LR test statistic well under small, moderate, and even severe misspecifications regardless of the sample size (as long as it is sufficiently large), whereas the normal distribution, with a bias correction, gives a slightly better approximation for extremely severe misspecifications. However, neither the noncentral chi-square distribution nor the theoretical normal distributions give a reasonable approximation of the LR test statistics under extremely severe misspecifications. Of course, extremely misspecified models are not of much practical interest. We also use the Thurstone data ( Thurstone & Thurstone, 1941 ) from a classic study of mental ability for our illustration
Chi-square test · Goodness of fit · Monte Carlo method · Statistic · Statistical hypothesis testing · Statistics · Test statistic · Thurstone scale · Mathematics · Mental Health Research Topics · Psychometric Methodologies and Testing · Sensory Analysis and Statistical Methods
An Introduction to the Bootstrap
An Introduction to the Bootstrap
Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses
On the Multivariate Asymptotic Distribution of Sequential Chi-Square Statistics
Testing Structural Equation Models
Noncentral Chi-Square Versus Normal Distributions in Describing the Likelihood Ratio Statistic
Alternative Ways of Assessing Model Fit
Two Equivalent Discrepancy Functions for Maximum Likelihood Estimation
| Citations per year | 0.36 |
|---|---|
| Citation span | 2012 - 2023 (12) |
| Highly cited | No |