Journal ArticleDOI
Asymptotic expansion of the distributions of the estimators in factor analysis under non-normality
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Equations for the Edgeworth expansion of the distributions of the estimators in exploratory factor analysis and structural equation modeling and results show that asymptotic expansion gives substantial improvement of approximation to the exact distribution constructed by simulations over the usual normal approximation.Abstract:
Equations for the Edgeworth expansion of the distributions of the estimators in exploratory factor analysis and structural equation modeling are given. The equations cover the cases of non-normal data, as well as normal ones with and without known first-order asymptotic standard errors. When the standard errors are unknown, the distributions of the Studentized statistics are expanded. Methods of constructing confidence intervals of population parameters with arbitrary asymptotic confidence coefficients are given using the Cornish-Fisher expansion. Simulations are performed to see the usefulness of the asymptotic expansions in exploratory factor analysis with rotated solutions and confirmatory factor analysis. The results show that asymptotic expansion gives substantial improvement of approximation to the exact distribution constructed by simulations over the usual normal approximation.read more
Citations
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Journal ArticleDOI
Bias correction of the Akaike information criterion in factor analysis
TL;DR: Simulations for model selection give consistently improved results by the approximate correction of the higher-order bias for the AIC over the usual AIC.
Journal ArticleDOI
Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality
TL;DR: Asymptotic expansions of the distributions of typical estimators in canonical correlation analysis under nonnormality are obtained in this article, including the Edgeworth expansions up to order O(1/n) for the parameter estimators.
Journal ArticleDOI
Estimating Standard Errors in Exploratory Factor Analysis.
TL;DR: 6 issues influencing standard errors in exploratory factor analysis are described and 7 methods of computing standard errors for rotated factor loadings and factor correlations are reviewed.
Journal ArticleDOI
Higher-order approximations to the distributions of fit indexes under fixed alternatives in structural equation models
TL;DR: In this paper, higher-order approximations to the distributions of fit indexes for structural equation models under fixed alternative hypotheses are obtained in nonnormal samples as well as normal ones.
Journal ArticleDOI
Asymptotic expansions in mean and covariance structure analysis
TL;DR: Simulations are performed for a factor analysis model with nonzero factor means to see the accuracy of the asymptotic expansions of the parameter estimators standardized by the population asymPTotic standard errors in finite samples.
References
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Journal ArticleDOI
A general approach to confirmatory maximum likelihood factor analysis
TL;DR: In this paper, the authors describe a general procedure by which any number of parameters of the factor analytic model can be held fixed at any values and the remaining free parameters estimated by the maximum likelihood method.
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An approximate method for generating asymmetric random variables
TL;DR: A method for generating values of continuous symmetric random variables that is relatively fast, requires essentially no computer memory, and is easy to use is developed.
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Alternative Test Criteria in Covariance Structure Analysis: A Unified Approach.
TL;DR: In this paper, a unified approach to the asymptotic theory of alternative test criteria for testing parametric restrictions is provided, and the discussion develops within a general framework that distinguishes whether or not the fitting function is a chi-square distribution, and allows the null and alternative hypothesis to be only approximations of the true model.
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Robustness of normal theory methods in the analysis of linear latent variate models.
TL;DR: In this paper, the covariance matrix of sample covariances under the class of linear latent variate models is derived using properties of cumulants, and conditions for normal theory estimators and test statistics to retain their usual asymptotic properties under non-normality of latent variates are given.