### Abstract

A structural measurement model (Adams, Wilson, & Wu, 1997) consists of an item response theory model for responses conditional on ability and a structural model that describes the distribution of ability in the population. As a rule, ability is assumed to be normally distributed in the population. However, there are situations where there is reason to assume that the distribution of ability is nonnormal. In this paper, we show that nonnormal ability distributions are easily modeled in a Bayesian framework

Original language | Undefined |
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Title of host publication | Psychometrics in practice at RCEC |

Editors | Theodorus Johannes Hendrikus Maria Eggen, Bernard P. Veldkamp |

Publisher | RCEC |

Pages | 103-114 |

ISBN (Print) | 9789036533744 |

DOIs | |

Publication status | Published - 2012 |

### Publication series

Name | |
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Publisher | RCEC |

### Keywords

- Item Response Theory
- one-parameter logistic model
- finite mixture
- Markov chain Monte Carlo
- plausible values
- IR-80205
- Bayes estimates
- Gibbs sampler

## Cite this

Marsman, M., Maris, G., & Bechger, T. (2012). Don't Tie Yourself to an Onion: Don’t Tie Yourself to Assumptions of Normality. In T. J. H. M. Eggen, & B. P. Veldkamp (Eds.),

*Psychometrics in practice at RCEC*(pp. 103-114). RCEC. https://doi.org/10.3990/3.9789036533744.ch8