### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 671-684 |

Number of pages | 13 |

Journal | Psychometrika |

Volume | 70 |

Issue number | 4 |

DOIs | |

Publication status | Published - 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

*Psychometrika*,

*70*(4), 671-684. https://doi.org/10.1007/s11336-001-0929-2

}

*Psychometrika*, vol. 70, no. 4, pp. 671-684. https://doi.org/10.1007/s11336-001-0929-2

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

Research output: Contribution to journal › Article › Academic › peer-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

Y1 - 2005

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.

KW - METIS-230410

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

KW - IR-60244

U2 - 10.1007/s11336-001-0929-2

DO - 10.1007/s11336-001-0929-2

M3 - Article

VL - 70

SP - 671

EP - 684

JO - Psychometrika

JF - Psychometrika

SN - 0033-3123

IS - 4

ER -