Abstract
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.
Highlights
Several logit-link regression models have been proposed to deal with ordered categorical response data
The purpose of this paper is to investigate the practicality of fitting the ordinal models with a logarithmic link in place of the logit link
We refer to the resulting models as the adjacent categories (AC) probability model, the continuation-ratio (CR) probability model, and the proportional probability (PP) model
Summary
Several logit-link regression models have been proposed to deal with ordered categorical response data. Three of these are the adjacent categories model [1], the continuation-ratio model [2], and the cumulative odds model [3]. The purpose of this paper is to investigate the practicality of fitting the ordinal models with a logarithmic link in place of the logit link. We refer to the resulting models as the adjacent categories (AC) probability model, the continuation-ratio (CR) probability model, and the proportional probability (PP) model. The ordinal log-link models make it possible to directly estimate different but related forms of the risk ratio in prospective studies and the prevalence ratio in cross-sectional studies, overcoming thereby a limitation of logit-link models.
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