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Sample Size Determination Within the Scope of Conditional Maximum Likelihood Estimation with Special Focus on Testing the Rasch Model

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  • Clemens Draxler
  • Rainer Alexandrowicz

Abstract

This paper refers to the exponential family of probability distributions and the conditional maximum likelihood (CML) theory. It is concerned with the determination of the sample size for three groups of tests of linear hypotheses, known as the fundamental trinity of Wald, score, and likelihood ratio tests. The main practical purpose refers to the special case of tests of the class of Rasch models. The theoretical background is discussed and the formal framework for sample size calculations is provided, given a predetermined deviation from the model to be tested and the probabilities of the errors of the first and second kinds. Copyright The Psychometric Society 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:4:p:897-919
    DOI: 10.1007/s11336-015-9472-y
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    References listed on IDEAS

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    Cited by:

    1. Clemens Draxler & Andreas Kurz, 2021. "Conditional Inference in Small Sample Scenarios Using a Resampling Approach," Stats, MDPI, vol. 4(4), pages 1-13, October.
    2. Felix Zimmer & Clemens Draxler & Rudolf Debelak, 2023. "Power Analysis for the Wald, LR, Score, and Gradient Tests in a Marginal Maximum Likelihood Framework: Applications in IRT," Psychometrika, Springer;The Psychometric Society, vol. 88(4), pages 1249-1298, December.
    3. Pedro Henrique Ribeiro Santiago & Rachel Roberts & Lisa Gaye Smithers & Lisa Jamieson, 2019. "Stress beyond coping? A Rasch analysis of the Perceived Stress Scale (PSS-14) in an Aboriginal population," PLOS ONE, Public Library of Science, vol. 14(5), pages 1-24, May.
    4. Alexander Robitzsch, 2021. "A Comprehensive Simulation Study of Estimation Methods for the Rasch Model," Stats, MDPI, vol. 4(4), pages 1-23, October.
    5. Clemens Draxler, 2018. "Bayesian conditional inference for Rasch models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 245-262, April.
    6. Clemens Draxler & Andreas Kurz & Can Gürer & Jan Philipp Nolte, 2024. "An Improved Inferential Procedure to Evaluate Item Discriminations in a Conditional Maximum Likelihood Framework," Journal of Educational and Behavioral Statistics, , vol. 49(3), pages 403-430, June.

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