## Abstract

We introduce a general response model that allows for several simple restrictions, resulting in other models such as the extended Rasch model. For the extended Rasch model, a dynamic Bayesian estimation procedure is provided, which is able to deal with data sets that change over time, and possibly include many missing values. To ensure comparability over time, a data augmentation method is used, which provides an augmented person-by-item data matrix and reproduces the sufficient statistics of the complete data matrix. Hence, longitudinal comparisons can be easily made based on simple summaries, such as proportion correct, sum score, etc. As an illustration of the method, an example is provided using data from a computer-adaptive practice mathematical environment.

Original language | English |
---|---|

Pages (from-to) | 72-87 |

Number of pages | 16 |

Journal | British Journal of Mathematical and Statistical Psychology |

Volume | 73 |

Issue number | 1 |

Early online date | 18 Mar 2019 |

DOIs | |

Publication status | Published - 1 Feb 2020 |

## Keywords

- computer-adaptive learning
- dynamic Bayesian estimation
- extended Rasch model
- network analysis
- smoothing
- time series