Some New Covariance Structure Model Improvement Statistics

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Abstract
Model modification in covariance structure analysis through reducing constraints can have an impact on the estimates of the maintained free parameters if the model is reevaluated. Three new statistics that focus on the estimated changes of parameter estimates and estimated sampling variability of the maintained free parameters are developed in this study. Another new statistic focuses on the significance of the estimated change in restricted, especially, fixed, parameters. An empirical investigation of the performance of these four new statistics showed that they can provide valuable supplementary information to the Lagrange multiplier statistic.