Customer Taste With Mixed Logit

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n n n
n n y P
g y P y h ⋅ = . Sampling variance in the estimator of θ
induces sampling variance in ) (⋅ h .
With linear models, where yn and n β are continuous, inference about observationspecific
coefficients within a random-coefficients context has been conducted extensively
for many years (e.g., Griffiths, 1972; Judge et al., 1989). Regime-switching models,
particularly in macroeconomics, have used the procedure described above to assess the
probability that an observation is within a given regime (e.g., Hamilton, 1996; Hamilton
and Susmel, 1994.) In these models, yn is continuous and n β is discrete. However, aside
from a redefinition of terms (e.g., ) (⋅ g and ) (⋅ h are probabilities rather than densities),
the procedure is the same, in that θ=
is estimated by maximum likelihood and the
probability of an observation being within a particular regime is inferred from the
estimate of θ=
using the formula
) | (
) | ( ) | ( ) , | (
θ
θ β β θ β
n
n n n
n n y P
g y P y h ⋅ = . For situations with
discrete yn, Bayesian methods have been developed that use Gibbs sampling to generate
draws of θ and n β from their posterior distribution (e.g., Rossi, McCulloch, and Allenby,
1996; Allenby and Rossi, 1999.) These methods are similar to ours in the inference
about n β given θ ; however, they use a Bayesian approach to estimation of θ while ours
is classical. In particular, we examine situations with discrete yn (like the cited Bayesian
studies) and use maximum likelihood methods (like the regime-switching models.) To
our knowledge, this is the first such application. Either continous or discrete n β can be
specified, though our empirical example uses only continuous n β . Also, we specify a
mixed logit model of customer choice; however, other behavioral specifications, such as
probit, could eas...