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The adjacent-categories, continuation-ratio and proportional oddslogit-link regression models provide useful extensions of the multinomiallogistic model to ordinal response data. We propose fitting these models with alogarithmic link to allow estimation of different forms of the risk ratio. Eachof the resulting ordinal response log-link models is a constrained version ofthe log multinomial model, the log-link counterpart of the multinomial logisticmodel. These models can be estimated using software that allows the user tospecify the log likelihood as the objective function to be maximized and toimpose constraints on the parameter estimates. In example data with adichotomous covariate, the unconstrained models produced valid coefficientestimates and standard errors, and the constrained models produced plausibleresults. Models with a single continuous covariate performed well in datasimulations, with low bias and mean squared error on average and appropriateconfidence interval coverage in admissible solutions. In an application to realdata, practical aspects of the fitting of the models are investigated. Weconclude that it is feasible to obtain adjusted estimates of the risk ratio forordinal outcome data.

KEYWORDS

Ordinal; Risk Ratio; Multinomial Likelihood; Logarithmic Link; Log Multinomial Regression; Adjacent Categories; Continuation-Ratio; Proportional Odds; Ordinal Logistic Regression

Cite this paper

C. Blizzard, S. Quinn, J. Canary and D. Hosmer -Log-Link Regression Models for Ordinal Responses,- Open Journal of Statistics, Vol. 3 No. 4A, 2013, pp. 16-25. doi: 10.4236-ojs.2013.34A003.





Autor: Christopher L. Blizzard, Stephen J. Quinn, Jana D. Canary, David W. Hosmer

Fuente: http://www.scirp.org/



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