Closed-form Bayesian inferences for the logit model via polynomial expansions

Steven Miller (), Eric Bradlow () and Kevin Dayaratna ()

Quantitative Marketing and Economics (QME), 2006, vol. 4, issue 2, 173-206

Abstract: Articles in Marketing and choice literatures have demonstrated the need for incorporating person-level heterogeneity into behavioral models (e.g., logit models for multiple binary outcomes as studied here). However, the logit likelihood extended with a population distribution of heterogeneity doesn’t yield closed-form inferences, and therefore numerical integration techniques are relied upon (e.g., MCMC methods). We present here an alternative, closed-form Bayesian inferences for the logit model, which we obtain by approximating the logit likelihood via a polynomial expansion, and then positing a distribution of heterogeneity from a flexible family that is now conjugate and integrable. For problems where the response coefficients are independent, choosing the Gamma distribution leads to rapidly convergent closed-form expansions; if there are correlations among the coefficients one can still obtain rapidly convergent closed-form expansions by positing a distribution of heterogeneity from a Multivariate Gamma distribution. The solution then comes from the moment generating function of the Multivariate Gamma distribution or in general from the multivariate heterogeneity distribution assumed. Closed-form Bayesian inferences, derivatives (useful for elasticity calculations), population distribution parameter estimates (useful for summarization) and starting values (useful for complicated algorithms) are hence directly available. Two simulation studies demonstrate the efficacy of our approach. Copyright Springer Science + Business Media, LLC 2006

Keywords: Closed-Form Bayesian Inferences; Logit model; Generalized Multivariate Gamma Distribution (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:kap:qmktec:v:4:y:2006:i:2:p:173-206

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DOI: 10.1007/s11129-006-8129-7

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