### Abstract

In latent theory the measurement properties of a mental test can be expressed in the test information function. The relative merits of two tests for the same latent trait can be described by the relative efficiency function, i.e. the ratio of the test information functions. It is argued that these functions have to be estimated if the values of the item difficulties are unknown. Using conditional maximum likelihood estimation as indicated by Andersen (1973), pointwise asymptotic distributions of the test information and relative efficiency function are derived for the case of dichotomously scored Rasch homogeneous items. Formulas for confidence intervals are derived from the asymptotic distributions. An application to a mathematics test is given and extensions to other latent trait models are discussed.

Original language | Undefined |
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Pages (from-to) | 91-107 |

Journal | Statistica Neerlandica |

Volume | 38 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1984 |

### Keywords

- test information
- IR-70654
- Latent Trait Theory

## Cite this

Oosterloo, S. J. (1984). Confidence intervals for test information and relative efficiency.

*Statistica Neerlandica*,*38*(2), 91-107. https://doi.org/10.1111/j.1467-9574.1984.tb01101.x