TITLE:
Log-Link Regression Models for Ordinal Responses
AUTHORS:
Christopher L. Blizzard, Stephen J. Quinn, Jana D. Canary, David W. Hosmer
KEYWORDS:
Ordinal; Risk Ratio; Multinomial Likelihood; Logarithmic Link; Log Multinomial Regression; Adjacent Categories; Continuation-Ratio; Proportional Odds; Ordinal Logistic Regression
JOURNAL NAME:
Open Journal of Statistics,
Vol.3 No.4A,
August
23,
2013
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.