Logit Regression for Bounded Responses

Abstract

In this chapter we introduce logit regression which accommodates responses that are limited or bounded above and below. For example, the likelihood of trying a new product can neither be negative nor greater than 100%. Market share is similarly limited to the range between 0 and 100%. Indicator 0–1 responses, such as “tried the product or not” and “voted Republican,” reflect probabilities, such as the probability of trying a new product, the probability of winning a game, or the probability of voting Republican. 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.