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Regression Modeling of Ordinal Data with Nonzero Baselines
Author(s) -
Xie Minge,
Simpson Douglas G.
Publication year - 1999
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.1999.00308.x
Subject(s) - ordinal data , ordinal regression , computer science , data set , binary data , regression analysis , logarithm , statistics , mathematics , binary number , data mining , algorithm , mathematical analysis , arithmetic
Summary. This paper develops regression models for ordinal data with nonzero control response probabilities. The models are especially useful in dose‐response studies where the spontaneous or natural response rate is nonnegligible and the dosage is logarithmic. These models generalize Abbott's formula, which has been commonly used to model binary data with nonzero background observations. We describe a biologically plausible latent structure and develop an EM algorithm for fitting the models. The EM algorithm can be implemented using standard software for ordinal regression. A toxicology data set where the proposed model fits the data but a more conventional model fails is used to illustrate the methodology.