On the estimators of model-based and maximal reliability

Haruhiko Ogasawara

Journal of Multivariate Analysis, 2009, vol. 100, issue 6, 1232-1244

Abstract: Four estimators of the reliability for a composite score based on the factor analysis model and five estimators of the maximal reliability for the composite are presented. When the Wishart maximum likelihood is used for the estimation of the model parameters, it is shown that the five estimators of maximal reliability are the same. Asymptotic cumulants of the estimators and their logarithmic transformations are derived under arbitrary distributions with possible model misspecification. The theoretical results considering model misspecification when a model does not hold are shown to be closer to their simulated values than those neglecting model misspecification. Simulations of the confidence intervals using the normal approximation based on the asymptotically distribution-free theory and the asymptotic expansion by Hall's method with variable transformation are performed.

Keywords: primary; 62E20 secondary; 62H25 Maximal reliability Factor analysis Asymptotic expansion Model misspecification Nonnormal data (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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