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Robustness of normal theory methods in the analysis of linear latent variate models
Author(s) -
Browne M. W.,
Shapiro A.
Publication year - 1988
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1988.tb00896.x
Subject(s) - latent class model , mathematics , random variate , covariance , estimator , robustness (evolution) , lisrel , covariance matrix , statistics , econometrics , statistical inference , inference , linear model , normality , structural equation modeling , computer science , random variable , artificial intelligence , biochemistry , chemistry , gene
The structure of the covariance matrix of sample covariances under the class of linear latent variate models is derived using properties of cumulants. This is employed to provide a general framework for robustness of statistical inference in the analysis of covariance structures arising from linear latent variate models. Conditions for normal theory estimators and test statistics to retain each of their usual asymptotic properties under non‐normality of latent variates are given. Factor analysis, LISREL and other models are discussed as examples.