Modified Distribution-Free Goodness-of-Fit Test Statistic
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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 used in covariance structure analysis is the asymptotically distribution-free (ADF) test statistic introduced by Browne (Br J Math Stat Psychol 37:62–83, 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 could 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.
Keywordscovariance structures distribution-free test statistic asymptotics Chi-square distribution ill-conditioned problem
Funding was provided for the third author by National Science Foundation (Grant No. CMMI1232623).
- Bellman, R. E. (1960). Introduction to matrix analysis. New York: McGraw-Hill Book Company.Google Scholar
- Boomsma, A., & Hoogland, J. J. (2001). The robustness of lisrel modeling revisited. In Structural equation modeling: Present and future: A Festschrift in Honor of Karl Jöreskog (pp. 139–168). Chicago: Scientific Software International.Google Scholar
- Byrne, B. M. (2012). Choosing structural equation modeling computer software: Snapshots of lisrel, eqs, amos, and mplus. In R. H. Hoyle (Ed.), Handbook of structural equation modeling, chap. 19 (pp. 307–324). New York: Guilford Press.Google Scholar