TY - JOUR
T1 - Fast variational bayes methods for multinomial probit models
AU - Loaiza-Maya, Rubén
AU - Nibbering, Didier
N1 - Publisher Copyright:
© 2022 American Statistical Association.
PY - 2023
Y1 - 2023
N2 - The multinomial probit model is often used to analyze choice behavior. However, estimation with existing Markov chain Monte Carlo (MCMC) methods is computationally costly, which limits its applicability to large choice datasets. This article proposes a variational Bayes method that is accurate and fast, even when a large number of choice alternatives and observations are considered. Variational methods usually require an analytical expression for the unnormalized posterior density and an adequate choice of variational family. Both are challenging to specify in a multinomial probit, which has a posterior that requires identifying restrictions and is augmented with a large set of latent utilities. We employ a spherical transformation on the covariance matrix of the latent utilities to construct an unnormalized augmented posterior that identifies the parameters, and use the conditional posterior of the latent utilities as part of the variational family. The proposed method is faster than MCMC, and can be made scalable to both a large number of choice alternatives and a large number of observations. The accuracy and scalability of our method is illustrated in numerical experiments and real purchase data with one million observations.
AB - The multinomial probit model is often used to analyze choice behavior. However, estimation with existing Markov chain Monte Carlo (MCMC) methods is computationally costly, which limits its applicability to large choice datasets. This article proposes a variational Bayes method that is accurate and fast, even when a large number of choice alternatives and observations are considered. Variational methods usually require an analytical expression for the unnormalized posterior density and an adequate choice of variational family. Both are challenging to specify in a multinomial probit, which has a posterior that requires identifying restrictions and is augmented with a large set of latent utilities. We employ a spherical transformation on the covariance matrix of the latent utilities to construct an unnormalized augmented posterior that identifies the parameters, and use the conditional posterior of the latent utilities as part of the variational family. The proposed method is faster than MCMC, and can be made scalable to both a large number of choice alternatives and a large number of observations. The accuracy and scalability of our method is illustrated in numerical experiments and real purchase data with one million observations.
KW - Large choice datasets
KW - Multinomial probit model
KW - Variational inference
UR - http://www.scopus.com/inward/record.url?scp=85142278014&partnerID=8YFLogxK
U2 - 10.1080/07350015.2022.2139267
DO - 10.1080/07350015.2022.2139267
M3 - Article
AN - SCOPUS:85142278014
SN - 0735-0015
VL - 41
SP - 1352
EP - 1363
JO - Journal of Business and Economic Statistics
JF - Journal of Business and Economic Statistics
IS - 4
ER -