time within a single store. We denote by x$_{ht}$ the J GLYPH<2> K matrix of attribute values, also called covariates, that agent h encounters at her t th choice event. The j th row of x$_{ht}$ is denoted x > $_{ht j}$. The outcome of this choice event is the observed categorical random variable y$_{ht}$ , which we represent as a J GLYPH<2> 1 indicator vector. We use the observed . x$_{ht}$ ; y$_{ht}$ / pairs to infer which attributes have the strongest as- sociation with item choice. To this end, let U$_{ht j}$ denote the utility that accrues to agent h if she chooses item j at her t th choice event. This approach, called a “random util- ity model” (Train 2003), assumes utility is a noisy linear function of the attributes: U$_{ht j}$ D GLYPH<12> > h x$_{ht j}$ C e$_{ht j}$ . Here, GLYPH<12>$_{h}$ is a K GLYPH<2> 1 vector of agent-specific “tastes” or “preference loadings” for the item attributes, and e$_{ht j}$ is a random error term representing unobserved utility. We assume that each agent, at each choice event, selects the item maximizing her utility. In the mixed multinomial logit model, we further assume the random error terms e$_{ht j}$ are iid from a Gumbel Type 2 distribution. The implied choice probabilities turn out to be (McFadden 1974). In discrete choice modeling, the right-hand side of (2) is called the “multinomial logit” distribution, denoted MNL . x$_{ht}$ ; GLYPH<12>$_{h}$ / . It is essentially the same as the multi-logistic function used in polychotomous logistic regression, and it is often called the soft-max function in machine learning research. We further assume that GLYPH<12>$_{1:}$$_{H}$ are iid from a K -variate normal distribution with mean vector GLYPH<16> and covariance matrix GLYPH<127> , which we write as N$_{K}$ .GLYPH<16> ; GLYPH<127>/ . For empirical Bayes estimation, the model is now completely specified: 5 P . y$_{ht j}$ D 1 j x$_{ht}$ ; GLYPH<12>$_{h}$ / D exp .GLYPH<12> > h x$_{ht j}$ / ∑ j 0 exp .GLYPH<12> > h x$_{ht j}$ 0 / ; j D 1 ; : : : ; J (2) y$_{ht}$ j x$_{ht}$ ; GLYPH<12>$_{h}$ ind GLYPH<24> MNL . x$_{ht}$ ; GLYPH<12>$_{h}$ / ; h D 1 ; : : : ; H ; t D 1 ; : : : ; T$_{h}$ ; (3) GLYPH<12>$_{h}$ j GLYPH<16> ; GLYPH<127> iid GLYPH<24> N$_{K}$ .GLYPH<16> ; GLYPH<127>/ ; h D 1 ; : : : ; H : (4)