Modified Distribution-Free Goodness of Fit Test Statistic

Chun, So Yeon; Browne, Michael W.; Shapiro, Alexander

doi:10.2139/ssrn.2697843

Cited by 3 publications

(26 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Related to this issue is also the tendency for Γ to be ill-conditioned (i.e., that the inverse ofΓ in eq. (1) has high variability (Chun et al, 2018;Huang & Bentler, 2015). One measure of ill-conditioning is the condition number cond(Γ) = δ max /δ min , where δ max and δ min are the largest and smallest eigenvalues of Γ.…”

Section: The Modified Adf Test Statisticmentioning

confidence: 99%

“…As a remedy to the well-known poor small-sample performance of ADF, Chun et al (2018) recently proposed some modifications to the original T ADF test statistic.…”

Section: Introductionmentioning

confidence: 99%

“…Undoubtedly the potential significance of this recent contribution is immense, especially given the current lack of a convincingly best test statistic that can be used with typical sample sizes. As indicated by Chun et al (2018), the proposed modification yields d − 1 new modified test statistics, where d is the model degrees of freedom. That is, for each integer m = 1, 2, .…”

Section: Introductionmentioning

confidence: 99%

“…In order to effectively utilize this newly proposed modified test statistic, a natural uncertainty for any applied researcher would be: Given a posited model and a set sample size, how should the number m of modified degrees of freedom be determined? Although Chun et al (2018) did sketch a heuristic for determining m, they did not report details on the performance of the recommended heuristic. Instead, they evaluated the performance of the modified test statistic at fixed values of m. Across three models, Chun et al (2018) tabulated the performance of T M (m) only for limited ranges of m. For instance, Model 3 had d = 189 degrees of freedom, and hence m may range from m = 1 to m = 188.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of this study is twofold: (i) to investigate how the choice of m actually affects the performance of T M (m) under realistic sample size conditions, and (ii) to investigate how to expressly choose the value of m. To accomplish these goals, we empirically evaluate how the heuristic proposed by Chun et al (2018) performs and subsequently propose and evaluate a new bootstrap-based approach for determining m.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Examining the Performance of the Modified ADF Goodness-of-fit Test Statistic in Structural Equation Models

Foldnes

Marcoulides

Olsson

2019

Structural Equation Modeling: A Multidisciplinary Journal

View full text Add to dashboard Cite

The asymptotically distribution-free (ADF) test statistic introduced in a landmark paper by Browne (1984) depends on very mild distributional assumptions and is theoretically superior to many other so-called robust tests available in structural equation modeling.The ADF test, however, often leads to model overrejection even at modest sample sizes. To overcome its poor small-sample performance, Chun, Browne, and Shapiro ( 2018) recently proposed a family of robust test statistics obtained by modifying the ADF statistic. This study investigates by simulation the performance of the new modified test statistics. The results revealed that although a few of the test statistics adequately controlled Type I error rates in each of the examined conditions, most performed quite poorly. This result underscores the importance of choosing a modified test statistic that performs well for specific examined conditions. A parametric bootstrap method is proposed for identifying such a best-performing modified test statistic. Through further simulation it is shown that the proposed bootstrap approach performs well.

show abstract

Section: The Modified Adf Test Statisticmentioning

confidence: 99%

“…As a remedy to the well-known poor small-sample performance of ADF, Chun et al (2018) recently proposed some modifications to the original T ADF test statistic.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Examining the Performance of the Modified ADF Goodness-of-fit Test Statistic in Structural Equation Models

Foldnes

Marcoulides

Olsson

2019

Structural Equation Modeling: A Multidisciplinary Journal

View full text Add to dashboard Cite

show abstract

The Effect of Latent and Error Non-Normality on Measures of Fit in Structural Equation Modeling

Jobst¹,

Auerswald²,

Moshagen³

2021

Educational and Psychological Measurement

View full text Add to dashboard Cite

Prior studies investigating the effects of non-normality in structural equation modeling typically induced non-normality in the indicator variables. This procedure neglects the factor analytic structure of the data, which is defined as the sum of latent variables and errors, so it is unclear whether previous results hold if the source of non-normality is considered. We conducted a Monte Carlo simulation manipulating the underlying multivariate distribution to assess the effect of the source of non-normality (latent, error, and marginal conditions with either multivariate normal or non-normal marginal distributions) on different measures of fit (empirical rejection rates for the likelihood-ratio model test statistic, the root mean square error of approximation, the standardized root mean square residual, and the comparative fit index). We considered different estimation methods (maximum likelihood, generalized least squares, and (un)modified asymptotically distribution-free), sample sizes, and the extent of non-normality in correctly specified and misspecified models to investigate their performance. The results show that all measures of fit were affected by the source of non-normality but with varying patterns for the analyzed estimation methods.

show abstract

Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator

Nguyên

Kühn

Esfahani

2022

Operations Research

View full text Add to dashboard Cite

Note. The best result in each experiment is highlighted in bold.The optimal solutions of many decision problems such as the Markowitz portfolio allocation and the linear discriminant analysis depend on the inverse covariance matrix of a Gaussian random vector. In “Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator,” Nguyen, Kuhn, and Mohajerin Esfahani propose a distributionally robust inverse covariance estimator, obtained by robustifying the Gaussian maximum likelihood problem with a Wasserstein ambiguity set. In the absence of any prior structural information, the estimation problem has an analytical solution that is naturally interpreted as a nonlinear shrinkage estimator. Besides being invertible and well conditioned, the new shrinkage estimator is rotation equivariant and preserves the order of the eigenvalues of the sample covariance matrix. If there are sparsity constraints, which are typically encountered in Gaussian graphical models, the estimation problem can be solved using a sequential quadratic approximation algorithm.

show abstract

Modified Distribution-Free Goodness of Fit Test Statistic

Cited by 3 publications

References 20 publications

Examining the Performance of the Modified ADF Goodness-of-fit Test Statistic in Structural Equation Models

Examining the Performance of the Modified ADF Goodness-of-fit Test Statistic in Structural Equation Models

The Effect of Latent and Error Non-Normality on Measures of Fit in Structural Equation Modeling

Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator

Contact Info

Product

Resources

About