Where:
F(Zi) = represents the value of the standard normal density function
associated with each possible value of the underlying index Zi.
Pi = the probability that an individual is a frequent user of nutritional
labeling given knowledge of the independent variables Xis
e = the base of natural logarithms approximately equal to 2.7182
Zi = the underlying index number or βXi
α = the intercept
And βXi is a linear combination of independent variables so that:
Zi= log [Pi∕(1-Pi)] = β о + β 1X1 +β 2X2 + . . . +β nXn + ε
Where:
i = 1,2,. . . ,n are observations
Zi = the unobserved index level or the log odds of choice for the ith
observation
Xn = the nth explanatory variable for the ith observation
β = the parameters to be estimated
ε = the error or disturbance term
The dependent variable Zi in the above equation is the logarithm of the probability that
a particular choice will be made. The parameter estimates do not directly represent the
effect of the independent variables. To obtain the estimators for continuous
explanatory variables in the logit model, the changes in probability that Yi = 1(Pi)
brought about by a change in the independent variable, Xij is given by:
(∂Pi/ ∂Xij) = [β j exp (-β Xij)] / [1+exp (-β Xij)] 2
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