## A Bayesian analysis of the multinomial probit model with . . . (2000)

Venue: | Journal of Econometrics |

Citations: | 51 - 1 self |

### BibTeX

@ARTICLE{McCulloch00abayesian,

author = {Robert McCulloch and Nicholas G. Polson and Peter E. Rossi},

title = {A Bayesian analysis of the multinomial probit model with . . .},

journal = {Journal of Econometrics},

year = {2000},

volume = {99},

pages = {173--193}

}

### OpenURL

### Abstract

We present a new prior and corresponding algorithm for Bayesian analysis of the multinomial probit model. Our new approach places a prior directly on the identi"ed parameter space. The key is the speci"cation of a prior on the covariance matrix so that the (1,1) element if "xed at 1 and it is possible to draw from the posterior using standard distributions. Analytical results are derived which can be used to aid in assessment of the prior. # 2000 Elsevier Science S.A. All rights reserved.

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Citation Context ...R.E. McCulloch et al. / Journal of Econometrics 99 (2000) 173}193 proposed the method of simulated moments and Hajivassiliou and McFadden (1990) have proposed the method of simulated scores (see also =-=Keane, 1994; and-=- Borsch-Supan and Hajivassiliou, 1993). A Bayesian analysis of the MNP model is given in McCulloch and Rossi (1994) (henceforth MR) (see also Nobile, 1998). The MNP model, as commonly speci"ed, h... |

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Citation Context ... al. / Journal of Econometrics 99 (2000) 173}193 proposed the method of simulated moments and Hajivassiliou and McFadden (1990) have proposed the method of simulated scores (see also Keane, 1994; and =-=Borsch-Supan and Hajivassiliou, 1993). A Ba-=-yesian analysis of the MNP model is given in McCulloch and Rossi (1994) (henceforth MR) (see also Nobile, 1998). The MNP model, as commonly speci"ed, has a vector of coe$cients � and a covarian... |

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Citation Context ...n. The improper prior on � can be used as a diagnostic for prior sensitivity, if desired. Other possible approaches to assessing priors directly on the identi"ed parameters include using the pr=-=ior of Barnard et al., 2000 (-=-see, also, in McCulloch and Rossi, 1996) and the approach of Chib et al. (1998). In the Barnard et al. approach, � is written as Diag(S)R Diag(S) and various priors are used on the standard deviatio... |

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Citation Context ...tatistics literature on covariance matrix estimation that a modest amount of shrinkage on the eigenvalues or correlations will produce estimators with good risk properties (see Yang and Berger, 1994; =-=Daniels and Kass, 1999).-=- Thus, an improper prior on � has at least three undesirable aspects: (1) it is actually a very informative prior on the smallest eigenvalue, (2) the sampling properties of Bayes estimators based on... |

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Citation Context ... the method of simulated scores (see also Keane, 1994; and Borsch-Supan and Hajivassiliou, 1993). A Bayesian analysis of the MNP model is given in McCulloch and Rossi (1994) (henceforth MR) (see also =-=Nobile, 1998). The MNP model, as co-=-mmonly speci"ed, has a vector of coe$cients � and a covariance matrix � as parameters. However, the parameters (�, �) are not fully identi"ed. The model is often identi"ed by se... |

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Citation Context ...nometrics 99 (2000) 173}193 Fig. 7. Posterior distribution of smallest eigenvalue } small dataset. model (the main competitor to the MNP) it is possible to assess the prior in a more natural way (see =-=Koop and Poirier, 1993-=-). For the more complicated MNP model prior assessment is a di$cult problem. If, for example, the researcher had prior information about the underlying utility maximization process leading to the mult... |

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Citation Context ...on process leading to the multinomial data it might be possible to specify a prior on the full set of parameters (�I and �I ) and actually use that data to learn about the unidenti"ed paramet=-=ers (see Poirier, 1998). S-=-ome investigators are uncomfortable with informative priors and would like to use improper priors. The NID approach cannot be used with improper priors on either � or �. The ID approach can easily... |

3 |
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Citation Context ... j corresponds to a set of coe$cients � , and use a prior � � &N(�M , < ). (16) � � In our view, this hierarchical model makes the most sense when applied to the identi"ed coe$cients =-=(see for example Rossi et al., 1996-=-). The IDsR.E. McCulloch et al. / Journal of Econometrics 99 (2000) 173}193 187 Fig. 6. Prior distributions of smallest eigenvalue. approach can be extended easily to handle a variety of hierarchical ... |

1 | Similarities and di!erences in brand purchase behavior across categories. Unpublished dissertation - Ainslie - 1998 |

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Citation Context ...(McCulloch et al., 1994) has already stimulated the use of this prior for switching regression models by Koop and Poirier (1997) and for strucutural equations models with limited dependent variables (=-=Li, 1996-=-). Jacquier et al. (1994) use this prior to model correlation between innovations in the level and volatility of time series. Ainslie (1998) uses the ID prior in an extension of the standard MNP model... |