Siddhartha Chib, Kenichi Shimizu
arXiv 23 Aug 2023 · Statistics — Methodology · 1 citations (OpenAlex)
arXiv:2308.12470 · PDF · DOI · OpenAlex · Extracted main text
A common assumption in the fitting of unordered multinomial response models for $J$ mutually exclusive categories is that the responses arise from the same set of $J$ categories across subjects. However, when responses measure a choice made by the subject, it is more appropriate to condition the distribution of multinomial responses on a subject-specific consideration set, drawn from the power set of ${1,2,\ldots,J}$. This leads to a mixture of multinomial response models governed by a probability distribution over the $J^{\ast} = 2^J -1$ consideration sets. We introduce a novel method for estimating such generalized multinomial response models based on the fundamental result that any mass distribution over $J^{\ast}$ consideration sets can be represented as a mixture of products of $J$ component-specific inclusion-exclusion probabilities. Moreover, under time-invariant consideration sets, the conditional posterior distribution of consideration sets is sparse. These features enable a scalable MCMC algorithm for sampling the posterior distribution of parameters, random effects, and consideration sets. Under regularity conditions, the posterior distributions of the marginal response probabilities and the model parameters satisfy consistency. The methodology is demonstrated in a longitudinal data set on weekly cereal purchases that cover $J = 101$ brands, a dimension substantially beyond the reach of existing methods.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | J. Chiang, S. Chib, and C. Narasimhan (1998) Markov chain monte carlo and models of consideration set and parameter heterogeneity | 0.961 | 9 | 5 | 89% |
| 2 | V. H. Aguiar and N. Kashaev (2024) Identification and estimation of discrete choice models with unobserved choice sets | 0.928 | 4 | 3 | 100% |
| 3 | D. B. Dunson and C. Xing (2009) Nonparametric Bayes modeling of multivariate categorical data | 0.909 | 8 | 5 | 75% |
| 4 | G. S. Crawford, R. Griffith, and A. Iaria (2021) A survey of preference estimation with unobserved choice set heterogeneity | 0.843 | 4 | 3 | 75% |
| 5 | E. Van Nierop, B. Bronnenberg, R. Paap, M. Wedel, and P. Franses (2010) Retrieving unobserved consideration sets from household panel data | 0.811 | 4 | 2 | 100% |
| 6 | S. Chib and E. Greenberg (1995) Understanding the Metropolis-Hastings algorithm | 0.644 | 3 | 2 | 67% |
| 7 | J. Abaluck and A. Adams-Prassl (2021) What do consumers consider before they choose? | 0.644 | 2 | 2 | 100% |
| 8 | I. Morozov, S. Seiler, X. Dong, and L. Hou (2021) Estimation of preference heterogeneity in markets with costly search | 0.644 | 2 | 2 | 100% |
| 9 | Y. Zeng, D. Pang, H. Zhao, and T. Wang (2023) A zero-inflated logistic normal multinomial model for extracting microbial compositions | 0.644 | 2 | 2 | 100% |
| 10 | M. S. Goeree (2008) Limited information and advertising in the us personal computer industry | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 60 scored citations.