Characteristics of Structural Equation Models which Affect the Power of the Likelihood Ratio Test

1988 ◽  
pp. 220-236 ◽  
Author(s):  
W. E. Saris ◽  
A. Satorra
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Ratio Test

On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints.

2006 ◽  
Vol 11 (4) ◽  
pp. 439-455 ◽  
Author(s):  
Reinoud D. Stoel ◽  
Francisca Galindo Garre ◽  
Conor Dolan ◽  
Godfried van den Wittenboer
Keyword(s):  
Structural Equation Modeling ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Structural Equation ◽  
Equation Modeling ◽  
Ratio Test ◽  
Boundary Constraints

scholarly journals ADMISSIBLE SIGNIFICANCE TESTS IN SIMULTANEOUS EQUATION MODELS

2017 ◽  
Vol 33 (3) ◽  
pp. 534-550
Author(s):  
Theodore W. Anderson
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Structural Equation ◽  
Alternative Hypothesis ◽  
Simultaneous Equation ◽  
Reduced Form ◽  
Ratio Test ◽  
Linear Transformations ◽  
Significance Level ◽  
Endogenous Variables

Consider testing the null hypothesis that a single structural equation has specified coefficients. The alternative hypothesis is that the relevant part of the reduced form matrix has proper rank, that is, that the equation is identified. The usual linear model with normal disturbances is invariant with respect to linear transformations of the endogenous and of the exogenous variables. When the disturbance covariance matrix is known, it can be set to the identity, and the invariance of the endogenous variables is with respect to orthogonal transformations. The likelihood ratio test is invariant with respect to these transformations and is the best invariant test. Furthermore it is admissible in the class of all tests. Any other test has lower power and/or higher significance level. In particular, this likelihood ratio test dominates a test based on the Two-Stage Least Squares estimator.

scholarly journals A Note on Likelihood Ratio Tests for Models with Latent Variables

Psychometrika ◽  
2020 ◽  
Author(s):  
Yunxiao Chen ◽  
Irini Moustaki ◽  
Haoran Zhang
Keyword(s):  
General Theory ◽  
Likelihood Ratio ◽  
Latent Variables ◽  
Latent Variable ◽  
Structural Equation ◽  
Degrees Of Freedom ◽  
Structural Equation Models ◽  
Regularity Conditions ◽  
Ratio Test ◽  
Nested Models

AbstractThe likelihood ratio test (LRT) is widely used for comparing the relative fit of nested latent variable models. Following Wilks’ theorem, the LRT is conducted by comparing the LRT statistic with its asymptotic distribution under the restricted model, a $$\chi ^2$$ χ 2 distribution with degrees of freedom equal to the difference in the number of free parameters between the two nested models under comparison. For models with latent variables such as factor analysis, structural equation models and random effects models, however, it is often found that the $$\chi ^2$$ χ 2 approximation does not hold. In this note, we show how the regularity conditions of Wilks’ theorem may be violated using three examples of models with latent variables. In addition, a more general theory for LRT is given that provides the correct asymptotic theory for these LRTs. This general theory was first established in Chernoff (J R Stat Soc Ser B (Methodol) 45:404–413, 1954) and discussed in both van der Vaart (Asymptotic statistics, Cambridge, Cambridge University Press, 2000) and Drton (Ann Stat 37:979–1012, 2009), but it does not seem to have received enough attention. We illustrate this general theory with the three examples.

A likelihood ratio test for detecting patterns of disease-marker association

1997 ◽  
Vol 61 (4) ◽  
pp. 335-350 ◽  
Author(s):  
A. P. MORRIS ◽  
J. C. WHITTAKER ◽  
R. N. CURNOW
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Ratio Test ◽  
Disease Marker

Empirical Test of the Efficiency of UK Covered Warrants Market: Stochastic Dominance and Likelihood Ratio Test Approach

2010 ◽  
Author(s):  
Zhuo Qiao ◽  
Christian de Peretti ◽  
Chia-Ying Chan ◽  
Wing-Keung Wong
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Stochastic Dominance ◽  
Empirical Test ◽  
Ratio Test
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