Modified Distribution-Free Goodness of Fit Test Statistic

17 Pages Posted: 3 Dec 2015 Last revised: 25 Dec 2015

See all articles by So Yeon Chun

So Yeon Chun

Georgetown University - Robert Emmett McDonough School of Business

Michael Browne

Ohio State University (OSU)

Alexander Shapiro

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE)

Date Written: December 1, 2015

Abstract

Covariance structure analysis and its structural equation modeling extensions have become one of the most widely used methodologies in social sciences such as psychology, education, and economics. An important issue in such analysis is to assess the goodness-of-fit of a model under analysis. One of the most popular test statistics is the asymptotically distribution free (ADF) test statistic introduced by Browne in 1984. The ADF statistic can be used to test models without any specific distribution assumption (e.g., multivariate normal distribution) of the observed data. Despite its advantage, it has been shown in various empirical studies that unless sample sizes are extremely large, this ADF statistic can perform very poorly in practice. In this paper, we provide a theoretical explanation for this phenomenon and further propose a modified test statistic that improves the performance in samples of realistic size. The proposed statistic deals with the possible ill conditioning of the involved large scale covariance matrices.

Keywords: covariance structures, distribution-free test statistic, asymptotics, chisquare distribution, ill-conditioned problem

Suggested Citation

Chun, So Yeon and Browne, Michael and Shapiro, Alexander, Modified Distribution-Free Goodness of Fit Test Statistic (December 1, 2015). Georgetown McDonough School of Business Research Paper No. 2697843. Available at SSRN: https://ssrn.com/abstract=2697843 or http://dx.doi.org/10.2139/ssrn.2697843

So Yeon Chun (Contact Author)

Georgetown University - Robert Emmett McDonough School of Business ( email )

3700 O Street, NW
Washington, DC 20057
United States

Michael Browne

Ohio State University (OSU) ( email )

Alexander Shapiro

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE) ( email )

765 Ferst Drive
Atlanta, GA 30332-0205
United States

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