Limited Information Goodness-of-fit Testing in Multidimensional Contingency Tables
AbstractWe 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 PearsonÃÂ´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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Springer in its journal Psychometrika.
Volume (Year): 71 (2006)
Issue (Month): 4 (December)
Contact details of provider:
Web page: http://www.springerlink.com/link.asp?id=112911
Other versions of this item:
- Alberto Maydeu, 2005. "Limited Information Goodness-Of-Fit Testing In Multidimensional Contingency Tables," Working Papers Economia wp05-12, Instituto de Empresa, Area of Economic Environment.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- 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.
- C. Glas & N. Verhelst, 1989. "Extensions of the partial credit model," Psychometrika, Springer, vol. 54(4), pages 635-659, September.
- Bengt Muthén, 1978. "Contributions to factor analysis of dichotomous variables," Psychometrika, Springer, vol. 43(4), pages 551-560, December.
- 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.
- Albert Maydeu-Olivares, 2006.
"Limited information estimation and testing of discretized multivariate normal structural models,"
Springer, vol. 71(1), pages 57-77, March.
- 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.
- 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.
- Anders Christoffersson, 1975. "Factor analysis of dichotomized variables," Psychometrika, Springer, vol. 40(1), pages 5-32, March.
- Karl Jöreskog, 1994. "On the estimation of polychoric correlations and their asymptotic covariance matrix," Psychometrika, Springer, vol. 59(3), pages 381-389, September.
- Cees Glas, 1999. "Modification indices for the 2-PL and the nominal response model," Psychometrika, Springer, vol. 64(3), pages 273-294, September.
- 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.
- David Thissen & Lynne Steinberg, 1986. "A taxonomy of item response models," Psychometrika, Springer, vol. 51(4), pages 567-577, December.
- Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer, vol. 47(2), pages 149-174, June.
- G. Iliopoulos & M. Kateri & I. Ntzoufras, 2009. "Bayesian Model Comparison for the Order Restricted RC Association Model," Psychometrika, Springer, vol. 74(4), pages 561-587, December.
- Alberto Maydeu-Olivares & Rosa Montaño, 2013. "How Should We Assess the Fit of Rasch-Type Models? Approximating the Power of Goodness-of-Fit Statistics in Categorical Data Analysis," Psychometrika, Springer, vol. 78(1), pages 116-133, January.
- Joe, Harry & Lee, Youngjo, 2009. "On weighting of bivariate margins in pairwise likelihood," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 670-685, April.
- Silvia cagnone & Stefania Mignani, 2007. "Assessing the goodness of fit of a latent variable model for ordinal data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 337-361.
- Vassilis Vasdekis & Silvia Cagnone & Irini Moustaki, 2012. "A Composite Likelihood Inference in Latent Variable Models for Ordinal Longitudinal Responses," Psychometrika, Springer, vol. 77(3), pages 425-441, July.
- Li Cai, 2010. "A Two-Tier Full-Information Item Factor Analysis Model with Applications," Psychometrika, Springer, vol. 75(4), pages 581-612, December.
- Jochen Ranger & Jorg-Tobias Kuhn, 2012. "A flexible latent trait model for response times in tests," Psychometrika, Springer, vol. 77(1), pages 31-47, January.
- Javier Revuelta, 2010. "Estimating Difficulty from Polytomous Categorical Data," Psychometrika, Springer, vol. 75(2), pages 331-350, June.
- Harry Joe & Alberto Maydeu-Olivares, 2010. "A General Family of Limited Information Goodness-of-Fit Statistics for Multinomial Data," Psychometrika, Springer, vol. 75(3), pages 393-419, September.
- Kim, Sung-Ho & Choi, Hyemi & Lee, Sangjin, 2009. "Estimate-based goodness-of-fit test for large sparse multinomial distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1122-1131, February.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).
If references are entirely missing, you can add them using this form.