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Log-Link Regression Models for Ordinal Responses


Blizzard, CL and Quinn, SJ and Canary, JD and Hosmer, DW, Log-Link Regression Models for Ordinal Responses, Open Journal of Statistics, 3, (4A) pp. 16-25. ISSN 2161-718X (2013) [Refereed Article]


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Licenced under Creative Commons Attribution 4.0 International (CC BY 4.0)

DOI: doi:10.4236/ojs.2013.34A003


The adjacent-categories, continuation-ratio and proportional odds logit-link regression models provide useful extensions of the multinomial logistic model to ordinal response data. We propose fitting these models with a logarithmic link to allow estimation of different forms of the risk ratio. Each of the resulting ordinal response log-link models is a con- strained version of the log multinomial model, the log-link counterpart of the multinomial logistic model. These models can be estimated using software that allows the user to specify the log likelihood as the objective function to be maxi- mized and to impose constraints on the parameter estimates. In example data with a dichotomous covariate, the uncon- strained models produced valid coefficient estimates and standard errors, and the constrained models produced plausible results. Models with a single continuous covariate performed well in data simulations, with low bias and mean squared error on average and appropriate confidence interval coverage in admissible solutions. In an application to real data, practical aspects of the fitting of the models are investigated. We conclude that it is feasible to obtain adjusted estimates of the risk ratio for ordinal outcome data.

Item Details

Item Type:Refereed Article
Keywords:Ordinal; Risk Ratio; Multinomial Likelihood; Logarithmic Link; Log Multinomial Regression; Adjacent Categories; Continuation-Ratio; Proportional Odds; Ordinal Logistic Regression
Research Division:Mathematical Sciences
Research Group:Statistics
Research Field:Biostatistics
Objective Division:Health
Objective Group:Other health
Objective Field:Other health not elsewhere classified
UTAS Author:Blizzard, CL (Professor Leigh Blizzard)
UTAS Author:Canary, JD (Dr Jana Canary)
ID Code:88805
Year Published:2013
Funding Support:National Health and Medical Research Council (1034482)
Deposited By:Menzies Institute for Medical Research
Deposited On:2014-02-17
Last Modified:2014-08-01
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