Robustness of Statistical Inference in Factor Analysis and Related Models
Copyright policy )Robustness of Statistical Inference in Factor Analysis and Related Models
In this paper the author considers a class of latent variable models which includes the unrestricted factor analysis model. In this class of models it is shown that normal theory tests of fit and sequential difference tests retain all their asymptotic properties when common factors are fixed or have nonnormal distributions. The minimum discrepancy test statistics and estimators considered include the usual likelihood ratio test statistic and maximum likelihood estimators. As a special case a conjecture of \textit{R. P. McDonald} [see Br. J. Math. Stat. Psychol. 32, 212-228 (1979; Zbl 0439.62038)] is proved which means that the usual normal theory likelihood ratio test statistic would still have an asymptotic chi-squared distribution when misapplied to the fixed common factor model because of its relationship with a test for conditional independence.
- University of South Africa South Africa
- Sewanee: The University of the South United States
unrestricted factor analysis model, maximum likelihood estimators, conditional independence, sequential difference tests, factor analysis, normal theory tests of fit, robustness, Factor analysis and principal components; correspondence analysis, minimum discrepancy test statistics and estimators, asymptotic chi-squared distribution, latent variable models, asymptotic properties, nonnormal distributions, normal theory likelihood ratio test statistic, likelihood ratio test statistic, Robustness and adaptive procedures (parametric inference), LISREL
unrestricted factor analysis model, maximum likelihood estimators, conditional independence, sequential difference tests, factor analysis, normal theory tests of fit, robustness, Factor analysis and principal components; correspondence analysis, minimum discrepancy test statistics and estimators, asymptotic chi-squared distribution, latent variable models, asymptotic properties, nonnormal distributions, normal theory likelihood ratio test statistic, likelihood ratio test statistic, Robustness and adaptive procedures (parametric inference), LISREL
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