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Yuan, Ke-Hai; Cheng, Ying; Zhang, Wei – Psychometrika, 2010
This paper studies changes of standard errors (SE) of the normal-distribution-based maximum likelihood estimates (MLE) for confirmatory factor models as model parameters vary. Using logical analysis, simplified formulas and numerical verification, monotonic relationships between SEs and factor loadings as well as unique variances are found.…
Descriptors: Factor Analysis, Statistical Analysis, Error of Measurement, Models
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Yuan, Ke-Hai; Chan, Wai – Psychometrika, 2005
The normal theory based maximum likelihood procedure is widely used in structural equation modeling. Three alternatives are: the normal theory based generalized least squares, the normal theory based iteratively reweighted least squares, and the asymptotically distribution-free procedure. When data are normally distributed and the model structure…
Descriptors: Mathematical Concepts, Structural Equation Models, Least Squares Statistics, Maximum Likelihood Statistics
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Yuan, Ke-Hai; Bentler, Peter M. – Psychometrika, 2004
Since data in social and behavioral sciences are often hierarchically organized, special statistical procedures for covariance structure models have been developed to reflect such hierarchical structures. Most of these developments are based on a multivariate normality distribution assumption, which may not be realistic for practical data. It is…
Descriptors: Statistical Analysis, Statistical Inference, Statistical Distributions, Multivariate Analysis
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Yuan, Ke-Hai; Bentler, Peter M. – Psychometrika, 2000
Adapts robust schemes to mean and covariance structures, providing an iteratively reweighted least squares approach to robust structural equation modeling. Each case is weighted according to its distance, based on first and second order moments. Test statistics and standard error estimators are given. (SLD)
Descriptors: Least Squares Statistics, Robustness (Statistics), Structural Equation Models
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Yuan, Ke-Hai; Bentler, Peter M. – Psychometrika, 2000
Studied whether the standard z-statistic that evaluates whether a factor loading is statistically necessary is correctly applied in such situations and more generally when the variables being analyzed are arbitrarily rescaled. An example illustrates that neither the factor loading estimates nor the standard error estimates possess scale…
Descriptors: Error of Measurement, Estimation (Mathematics), Mathematical Models, Maximum Likelihood Statistics