On the Large-Sample Bias, Variance, and Mean Squared Error of the Conventional Noncentrality Parameter Estimator of Covariance Structure Models

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Abstract
The conventional noncentrality parameter estimator of covariance structure models, which is currently implemented in widely circulated structural modeling programs (e. g., LISREL, EQS, AMOS, RAMONA), is shown to possess asymptotically potentially large bias, variance, and mean squared error (MSE). A formal expression for its large-sample bias is presented, and its large-sample variance and MSE are quantified. Based on these results, it is suggested that future research needs to develop means of possibly unbiased estimation of the noncentrality parameter, with smaller variance and MSE.