Blizzard et al Log-link regression models for ordinal responses.pdf (224.36 kB)
Log-Link Regression Models for Ordinal Responses
journal contributionposted on 2023-05-17, 22:05 authored by Christopher BlizzardChristopher Blizzard, Quinn, SJ, Canary, JD, Hosmer, DW
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.
National Health & Medical Research Council
Publication titleOpen Journal of Statistics
Department/SchoolMenzies Institute for Medical Research
PublisherScientific Research Publishing, Inc.
Place of publicationUnited States
Rights statementLicenced under Creative Commons Attribution 4.0 International (CC BY 4.0) http://creativecommons.org/licenses/by/4.0/