Professor Robert W. Walker |
Center for Applied Statistics and Department of Political Sciences, |
Title: What's Being Generalized by Generalized Ordered Regression Models |
Abstract: We
examine models that relax proportionality in cumulative ordered regression
models. Something fundamental
arising from ordered variables and stochastic ordering implies a
partitioning. Efforts to relax
proportionality also relax the ability to collapse an inherently
multidimensional problem to a partitioning of the (unidimensional)
real line. It is surprising and
unfortunate to find that deviations from proportionality are sufficient to
generate internal contradictions.
Relaxing proportional odds/parallelism requires other relevant and
significant changes in the underlying model that are nonnested. We prove a single theorem linking
continuous support and partitions of a latent space to show that for these
two characteristics to be simultaneously satisfied, the model must be the
proportional-odds model.
Conditioning on the adjacency that is closely related to the
partitioning is fruitful, but at this point we join the class of
continuation-ratio models.
Alternatively, |