Abstract
This paper describes a class ordinal regression models in which the link function has scale parameters that may be estimated along with the regression parameters. One motivation is to provide a plausible model for group level categorical responses. In this case a natural class of scaled link functions is obtained by treating the group level responses as threshold averages of possible correlated latent individual level variables. We find scaled link functions also arise naturally in other circumstances. Our methodology is illustrated through environmental risk assessment data where (correlated) individual level responses and group level responses are mixed.
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The research was supported by NSF contract DMS 95–05290, and National Institute of Statistical Sciences Cooperative Agreement CR819638 and CR820897 with the U.S. EPA. R. J. Carroll’s research was also supported by a grant from the National Cancer Institute (CA-57030). The authors thank Daniel Guth of the U.S. EPA for making available the data on tetrachloroethylene
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Xie, M., Simpson, D.G., Carroll, R.J. (1997). Scaled Link Functions for Heterogeneous Ordinal Response Data*. In: Gregoire, T.G., Brillinger, D.R., Diggle, P.J., Russek-Cohen, E., Warren, W.G., Wolfinger, R.D. (eds) Modelling Longitudinal and Spatially Correlated Data. Lecture Notes in Statistics, vol 122. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0699-6_3
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DOI: https://doi.org/10.1007/978-1-4612-0699-6_3
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