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A comparison of the lower bounds to the reliabilities of factor score estimators

By N.C. de Schipper


Sometimes the need arises to obtain estimates on latent variables in factor analysis. These estimates can be obtained using factor score estimators. Whenever, factor score estimators are used the reliability of those factor score estimators needs to be assessed. Hessen (2016) derived lower bounds to the reliabilities of Thurstone's, Bartlett's and McDonald's factor score estimators. This paper investigates conditions under which the lower bounds to reliability of these factor score estimators are different from each other. Furthermore, this study compares the performance of these lower bounds by assessing the bias and the mean squared error (MSE) under mild violations of multivariate skewness. Under regular circumstances it is found that the lower bound to reliability of the Thurstone factor score estimator is greater than or equal to McDonald's which is greater than or equal to Bartlett's. When comparing the lower bounds there seem to be no relevant differences regarding the bias and the MSE of the lower bounds. Also, the lower bounds contain little bias and are sufficiently precise given mild violations of multivariate skewness

Topics: reliability of factor score estimators, simulation study, bias, mean squared error
Year: 2016
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