Abstract
In this article we describe a modification of the robust chi-square test of fit that yields more accurate type I error rates when the estimated model is at the boundary of the admissible space.
Highlights
Jak et al [1] did not identify the source of the inflated type-I error and naturally cast doubt on the Mplus robust chi-square testing in general
If the covariate is divided by a factor of 10 or 1000, so will the derivative of the regression parameter, i.e., the derivative criterion can be manipulated into a false convergence itself. When such an example is estimated with the Mplus EM algorithm, the logcriterion will force the iterations to continue beyond the point of satisfying the derivative criterion and will reach the maximum-likelihood, while optimization methods, such as QN, based solely on the derivatives criterion, will fail
The results show that the modified correction number implemented in Mplus 8.7 yields accurate results for the robust chi-square test of fit with both the EMA and the QN algorithms
Summary
Jak et al [1] pointed out that the robust chi-square in Mplus produces a very high type-I error for certain two-level models. Several of the models estimated in Jak et al [1] are at the border of the admissible space, and those are exactly the models that exhibited the inflated type-I error. Jak et al [1] did not identify the source of the inflated type-I error and naturally cast doubt on the Mplus robust chi-square testing in general.
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