# Discrete choice probability equation help (in pre-algebraic terms please)?

1. Jun 9, 2010

### moonman239

As it says in the title, will anyone please give me the equation (in pre-algebraic terms) for discrete choice probability? I can see that the equation is P = Prob( Person n chooses Alternative i ) = G(xni, xnj(forall j inequal to i), sn, β),

where

xni is a vector of attributes of alternative i faced by person n,

"forall j inequal to i" is a vector of attributes of the other alternatives (other than i) faced by person n,

sn is a vector of characteristics of person n, and

β is a set of parameters that relate variables to probabilities, which are estimated statistically.

(I'm totally copying this off Wikipedia.) I'm baffled. What is G()?

2. Jun 11, 2010

### EnumaElish

G is a probability distribution function such as normal or logistic. See http://en.wikipedia.org/wiki/Discrete_choice#Consumer_Utility for an example from consumer utility. If $\epsilon$ is normally distributed, so is $\epsilon_{nj}-\epsilon_{ni}$ and therefore

$$P_{ni}=Prob\left\{\epsilon_{nj}-\epsilon_{ni} < \beta z_{ni}-\beta z_{nj}\right\} = G\left(\beta z_{ni}-\beta z_{nj}\right)$$

where G is the normal c.d.f.