Comparing the Conventional and Bootstrap Estimators of Noncentrality Parameter in Structural Equation Modeling
Date Issued
2015
Date
2015
Author(s)
Yang, Tian
Abstract
Noncentrality parameter (NCP) plays an important role in evaluating structural equation models. The present simulation study compared the behaviors of three estimators of NCP. Raykov (2000) showed that the conventional noncentrality parameter estimator possessed asymptotically potentially large bias, variance, and mean squared error, and further developed a bias-corrected bootstrap estimator (Raykov, 2005) as a possible alternative for the conventional estimator. The noncentrality parameter is based on the asymptotic distribution of the chi-square test statistic under alternative hypothesis and is affected by sample size and degree of model misspecification. This Monte Carlo research therefore systematically manipulated degree of model misspecification, sample size and model type to evaluate the performance of the conventional noncentrality parameter estimator (δ ̂), Raykov’s bias-corrected bootstrap estimator (δ ̂_bc) and another bias-corrected bootstrap estimator proposed in this study (δ ̃_bc). The results showed that degree of model misspecification demonstrated the largest effect on the bias, relative bias, standard deviation and root mean squared error of these three noncentrality parameter estimators, followed by sample size. Absolute relative bias of these three estimators decreased with increasing sample size and degree of model misspecification, while their standard deviations and root mean squared errors increased with larger sample sizes and more severe model misspecifications. Raykov’s δ ̂_bc showed little bias under true models and tended to underestimate the true NCP value in other conditions, resulting in large absolute relative bias compared to the other two estimators. Although the standard deviation of δ ̂_bc was less than δ ̂ and δ ̃_bc, its root mean squared error was larger due to its bias. The other two estimators, δ ̂ and δ ̃_bc, performed similarly. Their absolute biases, absolute relative biases and mean squared errors were smaller than δ ̂_bc except for true models and very mild model misspecifications. The conventional NCP estimator is thus recommended considering its ease of computation and the behaviors shown in this simulation study. Further development of alternative estimators for this critical quantity in structural equation modeling is also encouraged.
Subjects
noncentrality parameter
bootstrap
structural equation modeling
Type
thesis
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