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Limited Information Goodness-Of-Fit Testing In Multidimensional Contingency Tables

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ALBERTO MAYDEU () (Instituto de Empresa)

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Abstract

We introduce a family of goodness-of-fit statistics for testing composite null hypotheses in multidimensional contingency tables of arbitrary dimensions. These statistics are quadratic forms in marginal residuals up to order r. They are asymptotically chi-square under the null hypothesis when parameters are estimated using any consistent and asymptotically normal estimator. We show that when r is small (r = 2) the proposed statistics have more accurate empirical Type I errors and are more powerful than Pearson´s X2 for a widely used item response model. Also, we show that the proposed statistics are asymptotically chi-squared under the null hypothesis when applied to subtables.

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Paper provided by Instituto de Empresa, Area of Economic Environment in its series Working Papers Economia with number wp05-12.

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Length: 28 pages
Date of creation: Feb 2005
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Handle: RePEc:emp:wpaper:wp05-12

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  1. Albert Maydeu-Olivares, 2006. "Limited information estimation and testing of discretized multivariate normal structural models," Psychometrika, Springer, vol. 71(1), pages 57-77, March. [Downloadable!] (restricted)
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  2. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer, vol. 47(2), pages 149-174, June. [Downloadable!] (restricted)
  3. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer, vol. 46(4), pages 443-459, December. [Downloadable!] (restricted)
  4. Cees Glas, 1988. "The derivation of some tests for the rasch model from the multinomial distribution," Psychometrika, Springer, vol. 53(4), pages 525-546, December. [Downloadable!] (restricted)
  5. Bengt Muthén, 1978. "Contributions to factor analysis of dichotomous variables," Psychometrika, Springer, vol. 43(4), pages 551-560, December. [Downloadable!] (restricted)
  6. Cees Glas, 1999. "Modification indices for the 2-PL and the nominal response model," Psychometrika, Springer, vol. 64(3), pages 273-294, September. [Downloadable!] (restricted)
  7. Karl Jöreskog, 1994. "On the estimation of polychoric correlations and their asymptotic covariance matrix," Psychometrika, Springer, vol. 59(3), pages 381-389, September. [Downloadable!] (restricted)
  8. Maydeu-Olivares, Albert & Joe, Harry, 2005. "Limited- and Full-Information Estimation and Goodness-of-Fit Testing in 2n Contingency Tables: A Unified Framework," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1009-1020, September. [Downloadable!] (restricted)
  9. C. Glas & N. Verhelst, 1989. "Extensions of the partial credit model," Psychometrika, Springer, vol. 54(4), pages 635-659, September. [Downloadable!] (restricted)
  10. David Thissen & Lynne Steinberg, 1986. "A taxonomy of item response models," Psychometrika, Springer, vol. 51(4), pages 567-577, December. [Downloadable!] (restricted)
  11. Albert Maydeu-Olivares, 2001. "Limited information estimation and testing of Thurstonian models for paired comparison data under multiple judgment sampling," Psychometrika, Springer, vol. 66(2), pages 209-227, June. [Downloadable!] (restricted)
  12. R. Darrell Bock, 1972. "Estimating item parameters and latent ability when responses are scored in two or more nominal categories," Psychometrika, Springer, vol. 37(1), pages 29-51, March. [Downloadable!] (restricted)
  13. Anders Christoffersson, 1975. "Factor analysis of dichotomized variables," Psychometrika, Springer, vol. 40(1), pages 5-32, March. [Downloadable!] (restricted)
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