We discuss regression models for ordered responses, such as ratings of bonds, schooling attainment, or measures of subjective well-being. Commonly used models in this context are the ordered logit and ordered probit regression models. They are based on an underlying latent model with single index function and constant thresholds. We argue that these approa~ches are overly restrictive and preclude a flexible estimation of the effect of regressors on the discrete outcome probabilities. For example, the signs of the marginal probability effects can only change once when moving from the smallest category to the largest one. We then discuss several alternative models that overcome these limitations. An application illustrates the benefit of these alternatives.
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