Logit Regression for Bounded Dependent Variables
In this chapter we introduce logit regression, a particular type of nonlinear regression which accommodates responses which are limited, or bounded above and below. For example, the likelihood of trying a new product can neither be negative nor greater than one hundred percent. Market share is similarly limited to the range between zero and one hundred percent. In each of these cases, dependent response must be rescaled, acknowledging these boundaries. The odds ratio rescales probabilities or shares to a corresponding unbounded measure. The logit, or natural logarithm of an odds ratio, rescales responses, producing an S-shaped pattern, which reflects greater response among “fence sitters” with probabilities or shares that are mid-range.