Research

Currently I am working on three different research projects summarized as

1. Bayesian Pólya-Gamma (PG) estimation methods for mixed logit models.
2. Pólya-Gamma (PG) methods for models with count variables.
3. Estimable mixed probit (MXP) models as an alternative to the panel mixed logit models.

Mixed logit models (MXL) are credited with the ability to deal with the three most important limitations of the multinomial logit model (MNL) by “allowing for random taste variation, unrestricted substitution patterns, and correlation in unobserved factors over time” (Train, 2009). Thus, MXL has the potential to deal with IIA violations when the utilities of alternatives are correlated (e.g., red bus/blue bus). However, modeling correlation among the choices in MXL leads to substantial computational challenges.

Polson et al. (JASA, 2014) proposed the Pólya-Gamma (PG) method, a data augmentation strategy for fully Bayesian inference in models with binomial likelihoods. It is a direct analog of the simple latent-variable method of Albert and Chib (1993) for binary probit, although it uses a different missing data mechanism. The PG technique works for any model with binomial likelihood parameterized by log-odds, such as multinomial logit (MNL) or negative-binomial models (NB) for overdispersed count data.