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An order-preserving property of the maximum likelihood estimates for the Rasch model

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  • Bertoli-Barsotti, Lucio

Abstract

The paper proves that the maximum likelihood estimates of item and person parameters of the Rasch model preserve the order of item and person total scores. The result is valid for conditional and unconditional maximum likelihood estimation.

Suggested Citation

  • Bertoli-Barsotti, Lucio, 2003. "An order-preserving property of the maximum likelihood estimates for the Rasch model," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 91-96, January.
    • Handle: RePEc:eee:stapro:v:61:y:2003:i:1:p:91-96
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    References listed on IDEAS

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    1. Karl Klauer, 1991. "Exact and best confidence intervals for the ability parameter of the Rasch model," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 535-547, September.
    2. Bas Hemker & Klaas Sijtsma & Ivo Molenaar & Brian Junker, 1996. "Polytomous IRT models and monotone likelihood ratio of the total score," Psychometrika, Springer;The Psychometric Society, vol. 61(4), pages 679-693, December.
    3. Huynh Huynh, 1994. "A new proof for monotone likelihood ratio for the sum of independent bernoulli random variables," Psychometrika, Springer;The Psychometric Society, vol. 59(1), pages 77-79, March.
    4. D. Grayson, 1988. "Two-group classification in latent trait theory: Scores with monotone likelihood ratio," Psychometrika, Springer;The Psychometric Society, vol. 53(3), pages 383-392, September.
    5. 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.
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    Cited by:

    1. Francesca DE BATTISTI & Giovanna NICOLINI & Silvia SALINI, 2008. "Methodological overview of Rasch model and application in customer satisfaction survey data," Departmental Working Papers 2008-04, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

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