Journal ArticleDOI
Some contributions to efficient statistics in structural models: Specification and estimation of moment structures.
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TLDR
In this article, it is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary, and some asymptotically distribution-free efficient estimators for such arbitrary structural models are developed.Abstract:
Current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments (e.g., means and covariances), and to distribution theory based on multivariate normality. In psychometrics the multinormality assumption is often incorrect, so that statistical tests on parameters, or model goodness of fit, will frequently be incorrect as well. It is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary. Structural representations are developed for generalizations of the Bentler-Weeks, Joreskog-Keesling-Wiley, and factor analytic models. Some asymptotically distribution-free efficient estimators for such arbitrary structural models are developed. Limited information estimators are obtained as well. The special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail. The argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory, which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds. Many open research areas are described.read more
Citations
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Journal ArticleDOI
Cutoff criteria for fit indexes in covariance structure analysis : Conventional criteria versus new alternatives
Li-tze Hu,Peter M. Bentler +1 more
TL;DR: In this article, the adequacy of the conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice were examined, and the results suggest that, for the ML method, a cutoff value close to.95 for TLI, BL89, CFI, RNI, and G...
Journal ArticleDOI
Structural equation modeling in practice: a review and recommended two-step approach
TL;DR: In this paper, the authors provide guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development, and present a comprehensive, two-step modeling approach that employs a series of nested models and sequential chi-square difference tests.
Journal ArticleDOI
Comparative fit indexes in structural models
TL;DR: A new coefficient is proposed to summarize the relative reduction in the noncentrality parameters of two nested models and two estimators of the coefficient yield new normed (CFI) and nonnormed (FI) fit indexes.
Journal ArticleDOI
lavaan: An R Package for Structural Equation Modeling
TL;DR: The aims behind the development of the lavaan package are explained, an overview of its most important features are given, and some examples to illustrate how lavaan works in practice are provided.
Journal ArticleDOI
Fit indices in covariance structure modeling : Sensitivity to underparameterized model misspecification
Li-tze Hu,Peter M. Bentler +1 more
TL;DR: In this article, the sensitivity of maximum likelihood (ML), generalized least squares (GLS), and asymptotic distribution-free (ADF)-based fit indices to model misspecification, under conditions that varied sample size and distribution.
References
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Journal ArticleDOI
Significance tests and goodness of fit in the analysis of covariance structures
TL;DR: In this article, a general null model based on modified independence among variables is proposed to provide an additional reference point for the statistical and scientific evaluation of covariance structure models, and the importance of supplementing statistical evaluation with incremental fit indices associated with the comparison of hierarchical models.
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TL;DR: In this article, the authors present a survey of the use of truncated distributions in the context of unions and wages, and some results on truncated distribution Bibliography Index and references therein.
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Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
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The jackknife, the bootstrap, and other resampling plans
TL;DR: The Delta Method and the Influence Function Cross-Validation, Jackknife and Bootstrap Balanced Repeated Replication (half-sampling) Random Subsampling Nonparametric Confidence Intervals as mentioned in this paper.
Journal ArticleDOI
Linear Statistical Inference and its Applications
P. G. Moore,C. Radhakrishna Rao +1 more
TL;DR: The theory of least squares and analysis of variance has been studied in the literature for a long time, see as mentioned in this paper for a review of some of the most relevant works. But the main focus of this paper is on the analysis of variance.