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

  • ALBERTO MAYDEU

    ()

    (Instituto de Empresa)

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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File URL: http://latienda.ie.edu/working_papers_economia/WP05-12.pdf
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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
Date of revision:
Handle: RePEc:emp:wpaper:wp05-12
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  1. David J. Bartholomew & Panagiota Tzamourani, 1999. "The Goodness of Fit of Latent Trait Models in Attitude Measurement," Sociological Methods & Research, , vol. 27(4), pages 525-546, May.
  2. 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.
  3. Anders Christoffersson, 1975. "Factor analysis of dichotomized variables," Psychometrika, Springer, vol. 40(1), pages 5-32, March.
  4. Alberto Maydeu, 2003. "Limited Information Estimation and Testing of Discretized Multivariate Normal Structural Models," Working Papers Economia wp03-03, Instituto de Empresa, Area of Economic Environment.
  5. 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.
  6. Bengt Muthén, 1978. "Contributions to factor analysis of dichotomous variables," Psychometrika, Springer, vol. 43(4), pages 551-560, December.
  7. 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.
  8. 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.
  9. Karl Jöreskog, 1994. "On the estimation of polychoric correlations and their asymptotic covariance matrix," Psychometrika, Springer, vol. 59(3), pages 381-389, September.
  10. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer, vol. 47(2), pages 149-174, June.
  11. Cees Glas, 1999. "Modification indices for the 2-PL and the nominal response model," Psychometrika, Springer, vol. 64(3), pages 273-294, September.
  12. 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.
  13. David Thissen & Lynne Steinberg, 1986. "A taxonomy of item response models," Psychometrika, Springer, vol. 51(4), pages 567-577, December.
  14. Teugels, Jozef L, 1990. "Some representations of the multivariate Bernoulli and binomial distributions," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 256-268, February.
  15. C. Glas & N. Verhelst, 1989. "Extensions of the partial credit model," Psychometrika, Springer, vol. 54(4), pages 635-659, September.
  16. Bengt Muthén, 1984. "A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators," Psychometrika, Springer, vol. 49(1), pages 115-132, March.
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