Bayesian Analysis

Multiple-Shrinkage Multinomial Probit Models with Applications to Simulating Geographies in Public Use Data

Lane F. Burgette and Jerome P. Reiter

Full-text: Open access

Abstract

Multinomial outcomes with many levels can be challenging to model. Information typically accrues slowly with increasing sample size, yet the parameter space expands rapidly with additional covariates. Shrinking all regression parameters towards zero, as often done in models of continuous or binary response variables, is unsatisfactory, since setting parameters equal to zero in multinomial models does not necessarily imply “no effect.” We propose an approach to modeling multinomial outcomes with many levels based on a Bayesian multinomial probit (MNP) model and a multiple shrinkage prior distribution for the regression parameters. The prior distribution encourages the MNP regression parameters to shrink toward a number of learned locations, thereby substantially reducing the dimension of the parameter space. Using simulated data, we compare the predictive performance of this model against two other recently-proposed methods for big multinomial models. The results suggest that the fully Bayesian, multiple shrinkage approach can outperform these other methods. We apply the multiple shrinkage MNP to simulating replacement values for areal identifiers, e.g., census tract indicators, in order to protect data confidentiality in public use datasets.

Article information

Source
Bayesian Anal., Volume 8, Number 2 (2013), 453-478.

Dates
First available in Project Euclid: 24 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.ba/1369407560

Digital Object Identifier
doi:10.1214/13-BA816

Mathematical Reviews number (MathSciNet)
MR3066949

Zentralblatt MATH identifier
1329.62117

Keywords
Confidentiality Dirichlet process disclosure spatial synthetic

Citation

Burgette, Lane F.; Reiter, Jerome P. Multiple-Shrinkage Multinomial Probit Models with Applications to Simulating Geographies in Public Use Data. Bayesian Anal. 8 (2013), no. 2, 453--478. doi:10.1214/13-BA816. https://projecteuclid.org/euclid.ba/1369407560


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