Choice Model Simulation - Defining Choice Probabilities

Defining Choice Probabilities

Once the consumer utilities have been specified, the researcher can derive choice probabilities. Namely, the probability of the student choosing the Irish pub over the American pub is

\begin{align} P_i & = \Pr(U_i > U_a) = \Pr( \alpha P_i + \beta D_i + \varepsilon_i > \alpha P_a + \beta D_a + \varepsilon_a ) \\ & = \Pr( \varepsilon_i - \varepsilon_a > \alpha P_a + \beta D_a - \alpha P_i - \beta D_i ) \end{align}

Denoting the observed portion of the utility function as V,

(3)

In the end, discrete choice modeling comes down to specifying the distribution of (or ) and solving the integral over the range of to calculate . Extending this to more general situations with

  1. N consumers (n = 1, 2, …, N),
  2. J choices of consumption (j = 1, 2, …, J),

The choice probability of consumer n choosing j can be written as

(4)

for all i other than j

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