### Abstract

A method for estimating the parameters of the Rasch model is examined. The unknown quantities in this method are the item parameters and the distribution function of the latent trait over the population. In this sense, the method is equivalent to marginal maximum likelihood estimation. The new procedure is based on a method suggested by J. Kiefer and J. Wolfowitz (1956). Their conclusions are reviewed, and links to the Rasch model are specified. In marginal maximum likelihood estimation, the item parameters are estimated first, and then the prior distribution of the person parameters is estimated using these estimates. The proposed method illustrates that it is possible to estimate these two quantities together and arrive at consistent estimates.

Original language | Undefined |
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Place of Publication | Enschede, the Netherlands |

Publisher | University of Twente, Faculty Educational Science and Technology |

Publication status | Published - 1987 |

### Publication series

Name | OMD research report |
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Publisher | University of Twente, Faculty of Educational Science and Technology |

No. | 87-1 |

### Keywords

- Latent Trait Theory
- Secondary Education
- Secondary School Students
- Statistical Analysis
- Mathematical Models
- Foreign Countries
- Estimation (Mathematics)
- Equations (Mathematics)
- IR-104191
- Maximum Likelihood Statistics

## Cite this

Engelen, R. J. H. (1987).

*Semiparametric estimation in the Rasch model*. (OMD research report; No. 87-1). Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology.