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Power and Sample Size Considerations in Psychometrics

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Statistics and Simulation (IWS 2015)

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Abstract

An overview and discussion of the latest developments regarding power and sample size determination for statistical tests of assumptions of psychometric models are given. Theoretical as well as computational issues and simulation techniques, respectively, are considered. The treatment of the topic includes maximum likelihood and least squares procedures applied in the framework of generalized linear (mixed) models. Numerical examples and comparisons of the procedures to be introduced are quoted.

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References

  1. Agresti, A.: Categorical Data Analysis, 2nd edn. Wiley, New York (2002)

    Book  Google Scholar 

  2. Alexandrowicz, R.W., Draxler, C.: Testing the Rasch model with the conditional likelihood ratio test: sample size requirements and bootstrap algorithms. J. Stat. Distrib. Appl. 3, 1–25 (2016)

    MATH  Google Scholar 

  3. Andersen, E.B.: Asymptotic properties of conditional maximum likelihood estimators. J. R. Stat. Soc. Ser. B 32, 283–301 (1970)

    MathSciNet  MATH  Google Scholar 

  4. Barndorff-Nielsen, O.: Information and Exponential Families in Statistical Theory. Wiley, New York (1978)

    MATH  Google Scholar 

  5. Draxler, C.: Sample size determination for Rasch model tests. Psychometrika 75, 708–724 (2010)

    Article  MathSciNet  Google Scholar 

  6. Draxler, C., Alexandrowicz, R.W.: Sample size determination within the scope of conditional maximum likelihood estimation with special focus on testing the Rasch model. Psychometrika 80, 897–919 (2015)

    Article  MathSciNet  Google Scholar 

  7. Draxler, C., Zessin, J.: The power function of conditional tests of the Rasch model. Adv. Stat. Anal. 99, 367–378 (2015)

    Article  MathSciNet  Google Scholar 

  8. Fischer, G.H., Molenaar, I.W.: Rasch Models-Foundations, Recent Developments and Applications. Springer, New York (1995)

    MATH  Google Scholar 

  9. Fleiss, J.L.: Statistical Methods for Rates and Proportions, 2nd edn. Wiley, New York (1981)

    MATH  Google Scholar 

  10. Haberman, S.J.: Tests for independence in two-way contingency tables based on canonical correlation and on linear-by-linear interaction. Ann. Stat. 9, 1178–1186 (1981)

    Article  MathSciNet  Google Scholar 

  11. Kubinger, K.D., Rasch, D., Yanagida, T.: On designing data-sampling for Rasch model calibrating an achievement test. Psychol. Sci. Q. 51, 370–384 (2009)

    Google Scholar 

  12. Kubinger, K.D., Rasch, D., Yanagida, T.: A new approach for testing the Rasch model. Educ. Res. Eval. 17, 321–333 (2011)

    Article  Google Scholar 

  13. Maydeu-Olivares, A., Montano, R.: How should we assess the fit of Rasch-type models? approximating the power of goodness-of-fit statistics in categorical data analysis. Psychometrika 78, 116–133 (2013)

    Article  MathSciNet  Google Scholar 

  14. McCullagh, P., Nelder, J.A.: Generalized Linear Models, 2nd edn. Chapman & Hall, New York (1989)

    Book  Google Scholar 

  15. Nelder, J.A., Wedderburn, R.W.M.: Generalized linear models. J. R. Stat. Soc. Ser. A 135, 370–384 (1972)

    Article  Google Scholar 

  16. Neyman, J., Pearson, E.S.: On the use and interpretation of certain test criteria for purposes of statistical inference. Biometrika 20A, 263–294 (1928)

    MATH  Google Scholar 

  17. Neyman, J., Pearson, E.S.: On the problem of the most efficient tests of statistical hypotheses. Philos. Trans. R. Soc. Lond. Ser. A Contain. Pap. Math. Phys. Character 231, 289–337 (1933)

    Article  Google Scholar 

  18. Pfanzagl, J.: On the consistency of conditional maximum likelihood estimators. Ann. Inst. Stat. Math. 45, 703–719 (1993)

    Article  MathSciNet  Google Scholar 

  19. Ponocny, I.: Nonparametric goodness-of-fit tests for the Rasch model. Psychometrika 66, 437–460 (2001)

    Article  MathSciNet  Google Scholar 

  20. Rao, C.R.: Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Proc. Camb. Philos. Soc. 44, 50–57 (1948)

    Article  MathSciNet  Google Scholar 

  21. Rao, C.R., Sinharay, S.: Psychometrics. Handbook of Statistics, vol. 26. Elsevier, Amsterdam (2007)

    MATH  Google Scholar 

  22. Rasch, D., Rusch, T., Simeckova, M., Kubinger, K.D., Moder, K., Simecek, P.: Tests of additivity in mixed and fixed effect two-way ANOVA models with single sub-class numbers. Stat. Pap. 50, 905–916 (2009)

    Article  MathSciNet  Google Scholar 

  23. Rasch, G.: Probabilistic models for some intelligence and attainment tests. Copenhagen: The Danish Institute of Education Research (1980). (Expanded Edition, 1980. Chicago: University of Chicago Press)

    Google Scholar 

  24. Silvey, S.D.: The Lagrangian multiplier test. Ann. Math. Stat. 30, 389–407 (1959)

    Article  MathSciNet  Google Scholar 

  25. Verhelst, N.D.: An efficient MCMC algorithm to sample binary matrices with fixed marginals. Psychometrika 73, 705–728 (2008)

    Article  MathSciNet  Google Scholar 

  26. Verhelst, N.D., Hatzinger, R., Mair, P.: The Rasch sampler. J. Stat. Softw. 20, 1–14 (2007)

    Article  Google Scholar 

  27. Wald, A.: Test of statistical hypotheses concerning several parameters when the number of observations is large. Trans. Am. Math. Soc. 54, 426–482 (1943)

    Article  MathSciNet  Google Scholar 

  28. Wilks, S.S.: The large sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Stat. 9, 60–62 (1938)

    Article  Google Scholar 

  29. Yanagida, T., Steinfeld, J.: pwrRasch: Statistical power simulation for testing the Rasch model. R package version 0.1-2 (2015). http://CRAN.R-project.org/package=pwrRasch

  30. Yanagida, T., Kubinger, K.D., Rasch, D.: Planning a study for testing the Rasch model given missing values due to the use of test-booklets. J. Appl. Meas. 16, 432–444 (2015)

    Google Scholar 

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Correspondence to Clemens Draxler .

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Draxler, C., Kubinger, K.D. (2018). Power and Sample Size Considerations in Psychometrics. In: Pilz, J., Rasch, D., Melas, V., Moder, K. (eds) Statistics and Simulation. IWS 2015. Springer Proceedings in Mathematics & Statistics, vol 231. Springer, Cham. https://doi.org/10.1007/978-3-319-76035-3_3

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