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Conditional Inference in Small Sample Scenarios Using a Resampling Approach

Author

Listed:
  • Clemens Draxler

    (Institute of Psychology, UMIT—Private University for Health Sciences Medical Informatics and Technology GmbH, 6060 Hall in Tirol, Austria)

  • Andreas Kurz

    (Institute of Psychology, UMIT—Private University for Health Sciences Medical Informatics and Technology GmbH, 6060 Hall in Tirol, Austria)

Abstract

This paper discusses a non-parametric resampling technique in the context of multidimensional or multiparameter hypothesis testing of assumptions of the Rasch model. It is based on conditional distributions and it is suggested in small sample size scenarios as an alternative to the application of asymptotic or large sample theory. The exact sampling distribution of various well-known chi-square test statistics like Wald, likelihood ratio, score, and gradient tests as well as others can be arbitrarily well approximated in this way. A procedure to compute the power function of the tests is also presented. A number of examples of scenarios are discussed in which the power function of the test does not converge to 1 with an increasing deviation of the true values of the parameters of interest from the values specified in the hypothesis to be tested. Finally, an attempt to modify the critical region of the tests is made aiming at improving the power and an R package is provided.

Suggested Citation

  • Clemens Draxler & Andreas Kurz, 2021. "Conditional Inference in Small Sample Scenarios Using a Resampling Approach," Stats, MDPI, vol. 4(4), pages 1-13, October.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:4:p:49-849:d:656772
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    References listed on IDEAS

    as
    1. Clemens Draxler & Johannes Zessin, 2015. "The power function of conditional tests of the Rasch model," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 367-378, July.
    2. Ivo Ponocny, 2001. "Nonparametric goodness-of-fit tests for the rasch model," Psychometrika, Springer;The Psychometric Society, vol. 66(3), pages 437-459, September.
    3. Gerhard Fischer, 1981. "On the existence and uniqueness of maximum-likelihood estimates in the Rasch model," Psychometrika, Springer;The Psychometric Society, vol. 46(1), pages 59-77, March.
    4. Mair, Patrick & Hatzinger, Reinhold, 2007. "Extended Rasch Modeling: The eRm Package for the Application of IRT Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i09).
    5. Norman Verhelst, 2008. "An Efficient MCMC Algorithm to Sample Binary Matrices with Fixed Marginals," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 705-728, December.
    6. Tom Snijders, 1991. "Enumeration and simulation methods for 0–1 matrices with given marginals," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 397-417, September.
    7. Clemens Draxler & Rainer Alexandrowicz, 2015. "Sample Size Determination Within the Scope of Conditional Maximum Likelihood Estimation with Special Focus on Testing the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 897-919, December.
    8. Yuguo Chen & Dylan Small, 2005. "Exact tests for the rasch model via sequential importance sampling," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 11-30, March.
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