2.5. The Logit Model
Now we’re ready to introduce the logit model, otherwise known as the logistic regression model. As we discussed earlier, a major problem with the linear probability model is that probabilities are bounded by 0 and 1, but linear functions are inherently unbounded. The solution is to transform the probability so that it’s no longer bounded.
Transforming the probability to an odds removes the upper bound. If we then take the logarithm of the odds, we also remove the lower bound. Setting the result equal to a linear function of the explanatory variables, we get the logit model. For k explanatory variables and i = 1,..., n individuals, the model is
Equation 2.3
where pi is, as before, the probability that yi=1. The expression ...
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