Regression models for unconstrained, partially or fully constrained continuation odds ratios

Epidemiologists frequently encounter studies with ordered responses. Standard ordered response logit models, such as the continuation ratio model, constrain exposure to have a homogeneous effect across thresholds of the ordered response. We demonstrate a method for fitting regression models for unconstrained, partially or fully constrained continuation odds ratios using a 'person-threshold' data set. For each subject, we create a separate record for each response threshold the subject is 'at risk' of passing and then apply standard binary logistic regression to estimate the continuation-ratio model. An example demonstrates the unconstrained, partially and fully constrained continuation-ratio model, while a small simulation study examines some properties of the proposed 'person-threshold' approach. Finally, we present a brief discussion of statistical software to implement the method.