Improving parameter tests in covariance structure analysis

Abstract

In many areas, covariance structure analysis plays an important role in understanding how the relationship among observed variables might be generated by hypothesized latent variables. Once a model is established as relevant to a given data set, it is important to evaluate the significance of specific parameters, such as coefficients of regressions among latent variables, within the model. The popular z-test of a parameter is the estimator of the parameter divided by its standard error estimator. A valid z-statistic must be based on a high-quality standard error estimator. We focus on the quality of the standard error estimator from both MLE and ADF methods, which are the two most frequently used methods in covariance structure practice. For these two estimation methods, empirical evidence shows that classical formulae give “too optimistic” standard error estimators, with the result that the z-tests regularly give false conclusions. We review one and introduce another simple corrected standard error estimator. These substantially improve on the classical ones, depending on distribution and sample size. Two implications of this study are that significant parameters as printed in most statistical software may not be really significant, and that corrected standard errors should be direct output for the two most widely used methods. A comparison of the accuracy of the estimators based on these two methods is also made.