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Location—scale cumulative odds models for ordinal data: A generalized non‐linear model approach
Author(s) -
Cox Christopher
Publication year - 1995
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780141105
Subject(s) - ordinal regression , generalized linear model , statistics , ordinal data , odds , mathematics , multinomial logistic regression , linear model , linear regression , goodness of fit , econometrics , generalization , context (archaeology) , regression analysis , computer science , logistic regression , mathematical analysis , paleontology , biology
Proportional odds regression models for multinomial probabilities based on ordered categories have been generalized in two somewhat different directions. Models having scale as well as location parameters for adjustment of boundaries (on an unobservable, underlying continuum) between categories have been employed in the context of ROC analysis. Partial proportional odds models, having different regression adjustments for different multinomial categories, have also been proposed. This paper considers a synthesis and further generalization of these two families. With use of a number of examples, I discuss and illustrate properties of this extended family of models. Emphasis is on the computation of maximum likelihood estimates of parameters, asymptotic standard deviations, and goodness‐of‐fit statistics with use of non‐linear regression programs in standard statistical software such as SAS.