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Accurate distribution and its asymptotic expansion for the tetrachoric correlation coefficient

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  • Ogasawara, Haruhiko

Abstract

Accurate distributions of the estimator of the tetrachoric correlation coefficient and, more generally, functions of sample proportions for the 2 by 2 contingency table are derived. The results are obtained given the definitions of the estimators even when some marginal cell(s) are empty. Then, asymptotic expansions of the distributions of the parameter estimators standardized by the population asymptotic standard errors up to order O(1/n) and those of the studentized ones up to the order next beyond the conventional normal approximation are derived. The asymptotic results can be obtained in a much shorter computation time than the accurate ones. Numerical examples were used to illustrate advantages of the studentized estimator of Fisher's z transformation of the tetrachoric correlation coefficient.

Suggested Citation

  • Ogasawara, Haruhiko, 2010. "Accurate distribution and its asymptotic expansion for the tetrachoric correlation coefficient," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 936-948, April.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:4:p:936-948
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    References listed on IDEAS

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    1. Ogasawara, Haruhiko, 2007. "Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1726-1750, October.
    2. Ogasawara, Haruhiko, 2006. "Asymptotic expansion of the sample correlation coefficient under nonnormality," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 891-910, February.
    3. D. Divgi, 1979. "Calculation of the tetrachoric correlation coefficient," Psychometrika, Springer;The Psychometric Society, vol. 44(2), pages 169-172, June.
    4. Morton Brown & Jacqueline Benedetti, 1977. "On the mean and variance of the tetrachoric correlation coefficient," Psychometrika, Springer;The Psychometric Society, vol. 42(3), pages 347-355, September.
    5. Haruhiko Ogasawara, 2009. "Asymptotic cumulants of the parameter estimators in item response theory," Computational Statistics, Springer, vol. 24(2), pages 313-331, May.
    6. R. E. Odeh & J. O. Evans, 1974. "The Percentage Points of the Normal Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 23(1), pages 96-97, March.
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