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Conditional Statistical Inference with Multistage Testing Designs

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  • Robert Zwitser

  • Gunter Maris

Abstract

In this paper it is demonstrated how statistical inference from multistage test designs can be made based on the conditional likelihood. Special attention is given to parameter estimation, as well as the evaluation of model fit. Two reasons are provided why the fit of simple measurement models is expected to be better in adaptive designs, compared to linear designs: more parameters are available for the same number of observations; and undesirable response behavior, like slipping and guessing, might be avoided owing to a better match between item difficulty and examinee proficiency. The results are illustrated with simulated data, as well as with real data. Copyright The Psychometric Society 2015

Suggested Citation

  • Robert Zwitser & Gunter Maris, 2015. "Conditional Statistical Inference with Multistage Testing Designs," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 65-84, March.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:1:p:65-84
    DOI: 10.1007/s11336-013-9369-6
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    References listed on IDEAS

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    1. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    2. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    3. Frederic Lord, 1971. "A theoretical study of two-stage testing," Psychometrika, Springer;The Psychometric Society, vol. 36(3), pages 227-242, September.
    4. Erling Andersen, 1973. "A goodness of fit test for the rasch model," Psychometrika, Springer;The Psychometric Society, vol. 38(1), pages 123-140, March.
    5. Thomas Warm, 1989. "Weighted likelihood estimation of ability in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 427-450, September.
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    Cited by:

    1. Peter W. Rijn & Usama S. Ali & Hyo Jeong Shin & Sean-Hwane Joo, 2024. "Adjusted Residuals for Evaluating Conditional Independence in IRT Models for Multistage Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 89(1), pages 317-346, March.
    2. Anders Skrondal & Sophia Rabe-Hesketh, 2022. "The Role of Conditional Likelihoods in Latent Variable Modeling," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 799-834, September.
    3. Paul A. Jewsbury & Peter W. van Rijn, 2020. "IRT and MIRT Models for Item Parameter Estimation With Multidimensional Multistage Tests," Journal of Educational and Behavioral Statistics, , vol. 45(4), pages 383-402, August.

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