Modified Distribution-Free Goodness-of-Fit Test Statistic
| Autor: | Michael W. Browne, So Yeon Chun, Alexander Shapiro |
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| Rok vydání: | 2017 |
| Předmět: |
Applied Mathematics
05 social sciences 050401 social sciences methods Multivariate normal distribution Covariance 01 natural sciences Structural equation modeling 010104 statistics & probability 0504 sociology Goodness of fit Sample size determination Data Interpretation Statistical Multivariate Analysis Statistics Test statistic Computer Simulation 0101 mathematics Factor Analysis Statistical Monte Carlo Method General Psychology Statistic Statistical hypothesis testing |
| Zdroj: | Psychometrika. 83:48-66 |
| ISSN: | 1860-0980 0033-3123 |
| DOI: | 10.1007/s11336-017-9574-9 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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