Logit Regression for Bounded Responses
In this chapter we introduce logit 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. 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, we need to rescale dependent response, 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.
KeywordsNatural Composition Bounded Response Trial Intention Limited Dependent Variable Service Aspect
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