Checking the assumptions of Rasch's model for speed tests

M.G.H. Jansen, Cornelis A.W. Glas

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)

Abstract

Two new tests for a model for the response times on pure speed tests by Rasch (1960) are proposed. The model is based on the assumption that the test response times are approximately gamma distributed, with known index parameters and unknown rate parameters. The rate parameters are decomposed in a subject ability parameter and a test difficulty parameter. By treating the ability as a gamma distributed random variable, maximum marginal likelihood (MML) estimators for the test difficulty parameters and the parameters of the ability distribution are easily derived. Also the model tests proposed here pertain to the framework of MML. Two tests or modification indices are proposed. The first one is focused on the assumption of local stochastic independence, the second one on the assumption of the test characteristic functions. The tests are based on Lagrange multiplier statistics, and can therefore be computed using the parameter estimates under the null model. Therefore, model violations for all items and pairs of items can be assessed as a by-product of one single estimation run. Power studies and applications to real data are included as numerical examples.
Original languageUndefined
Pages (from-to)671-684
Number of pages13
JournalPsychometrika
Volume70
Issue number4
DOIs
Publication statusPublished - 2005

Keywords

  • METIS-230410
  • Speed test - Rasch model - Lagrange multiplier test - local stochastic independence - model fit - score test - test characteristic curve
  • IR-60244

Cite this

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Checking the assumptions of Rasch's model for speed tests. / Jansen, M.G.H.; Glas, Cornelis A.W.

In: Psychometrika, Vol. 70, No. 4, 2005, p. 671-684.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Checking the assumptions of Rasch's model for speed tests

AU - Jansen, M.G.H.

AU - Glas, Cornelis A.W.

PY - 2005

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N2 - Two new tests for a model for the response times on pure speed tests by Rasch (1960) are proposed. The model is based on the assumption that the test response times are approximately gamma distributed, with known index parameters and unknown rate parameters. The rate parameters are decomposed in a subject ability parameter and a test difficulty parameter. By treating the ability as a gamma distributed random variable, maximum marginal likelihood (MML) estimators for the test difficulty parameters and the parameters of the ability distribution are easily derived. Also the model tests proposed here pertain to the framework of MML. Two tests or modification indices are proposed. The first one is focused on the assumption of local stochastic independence, the second one on the assumption of the test characteristic functions. The tests are based on Lagrange multiplier statistics, and can therefore be computed using the parameter estimates under the null model. Therefore, model violations for all items and pairs of items can be assessed as a by-product of one single estimation run. Power studies and applications to real data are included as numerical examples.

AB - Two new tests for a model for the response times on pure speed tests by Rasch (1960) are proposed. The model is based on the assumption that the test response times are approximately gamma distributed, with known index parameters and unknown rate parameters. The rate parameters are decomposed in a subject ability parameter and a test difficulty parameter. By treating the ability as a gamma distributed random variable, maximum marginal likelihood (MML) estimators for the test difficulty parameters and the parameters of the ability distribution are easily derived. Also the model tests proposed here pertain to the framework of MML. Two tests or modification indices are proposed. The first one is focused on the assumption of local stochastic independence, the second one on the assumption of the test characteristic functions. The tests are based on Lagrange multiplier statistics, and can therefore be computed using the parameter estimates under the null model. Therefore, model violations for all items and pairs of items can be assessed as a by-product of one single estimation run. Power studies and applications to real data are included as numerical examples.

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KW - Speed test - Rasch model - Lagrange multiplier test - local stochastic independence - model fit - score test - test characteristic curve

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