文章基本信息

标题：Log-Link Regression Models for Ordinal Responses
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作者：Christopher L. Blizzard ; Stephen J. Quinn ; Jana D. Canary 等
期刊名称：Open Journal of Statistics
印刷版ISSN：2161-718X
电子版ISSN：2161-7198
出版年度：2013
卷号：3
期号：4A
页码：16-25
DOI：10.4236/ojs.2013.34A003
出版社：Scientific Research Publishing
摘要：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 constrained 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 maximized and to impose constraints on the parameter estimates. In example data with a dichotomous covariate, the unconstrained 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.
关键词：Ordinal; Risk Ratio; Multinomial Likelihood; Logarithmic Link; Log Multinomial Regression; Adjacent Categories; Continuation-Ratio; Proportional Odds; Ordinal Logistic Regression