### Abstract

An item response theory (IRT) model is used as a measurement error model for the dependent variable of a multilevel model where tests or questionnaires consisting of separate items are used to perform a measurement error analysis. The advantage of using latent scores as dependent variables of a multilevel model is that it offers the possibility of modeling response variation and measurement error and separating the influence of item difficulty and ability level. The two-parameter normal ogive model is used for the IRT model. It is shown that the stochastic EM (expectation-maximization) (SEM) algorithm can be used to estimate the parameters that are close to the maximum likelihood estimated. It turns out that this algorithm is easily implemented. This estimation procedure is compared to an implementation of the Gibbs sample in a Bayesian framework. Examples using real data from a Dutch primary school language test are given.

Original language | English |
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Place of Publication | Enschede |

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

Number of pages | 26 |

Publication status | Published - 2000 |

### Publication series

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

No. | 00-02 |

### Keywords

- Bayesian Statistics
- Error of Measurement
- Estimation (Mathematics)
- Item Response Theory
- Test Items
- IR-104137
- METIS-136401

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## Cite this

Fox, G. J. A. (2000).

*Stochastic EM for estimating the parameters of a multilevel IRT model*. (OMD research report; No. 00-02). Enschede: University of Twente, Faculty Educational Science and Technology.