## Bayesian Item Response Modeling: Theory and Applications (Google eBook)The purpose of the book is to serve as a handbook for measurement specialists as well as to serve as a textbook for students in classes on the Bayesian approach to modern test theory. The book will also serve as a guide to the authors’ computer software implementations that will be made available via a website. This software supports the computation of the various models described in the book and can support readers in their own developmental work in IRT using advanced Bayesian techniques/models. The software implementations will be made available in the popular statistical packages Splus and R. The implemented new functions are built on Fortran code that is linked to the Splus and R environments. This approach leads to considerable reduction of computation time. |

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### Contents

1 | |

2 Bayesian Hierarchical Response Modeling | 31 |

3 Basic Elements of Bayesian Statistics | 45 |

4 Estimation of Bayesian Item Response Models | 67 |

5 Assessment of Bayesian Item Response Models | 107 |

6 Multilevel Item Response Theory Models | 141 |

7 Random Item E ects Models | 193 |

8 Response Time Item Response Models | 227 |

9 Randomized Item Response Models | 255 |

289 | |

309 | |

### Common terms and phrases

ability parameters analysis assumed augmented data Bayes factor cognitive impairment computed conditional distribution conditional posterior corresponding country-speciﬁc covariance matrix cross-national deﬁned denoted diﬀerent diﬃculty parameters discrimination parameters Equation ﬁrst ﬁt ﬁxed function Gibbs sampling given graded response model hierarchical prior hyperparameters identiﬁed independent individual inferences inﬂuence item characteristics item diﬃculty item response data item response model item response theory iterations latent response latent variable level-1 likelihood logistic marginal likelihood marginal posterior MCMC scheme methods mixed eﬀects model MLIRT model model parameters multilevel model multivariate nested normal prior normally distributed p-value parameter values person parameters polytomous population posterior density posterior distribution posterior mean posterior predictive posterior probability prior distributions random eﬀects random item eﬀects randomized response Rasch model restricted sampling school eﬀects scores shrinkage speciﬁc statistical testlet threshold parameters two-parameter variance variation vector WinBUGS Yijk zero Zijk