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Abstract
Chi-square tests based on maximum likelihood (ML) estimation of covariance structures often tend to over-reject the null hypothesis, Σ = Σθ, particularly when the sample size is small. Reweighted least squares (RLS) provides a solution to this issue. In some models, the parameter vector must include means, variances, and covariances; however, the effectiveness of RLS in mean and covariance structures remains unexplored. This research investigates the extension of RLS to mean and covariance structures by evaluating a generalized least squares function using ML parameter estimates. A Monte Carlo simulation study was conducted to compare the statistical performance of ML and RLS with multivariate normal data. Based on empirical rejection frequencies and averages of test statistics, the findings demonstrate that RLS significantly outperforms ML in mean and covariance structure models when the sample sizes are small. However, RLS does not exhibit superior performance to ML in rejecting misspecified models.
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