10 Choosing the Link When Modelling a Dichotomous Outcome or an Ordinal Outcome

Oregon Convention Center 

When one has a dichotomous outcome for study, logistic regression continues to be the most widely used model. With this model, one is using the logit link to relate the outcome to a set of explanatory variables. Logistic regression permits the estimation of various functions of log odds including odds ratios. In the literature, one often sees odds interpreted as though they are probabilities. There are many concerning issues with such interpretations. For example, the odds ratio is further from the null than the comparable risk ratio. It is well known that the logit link is the canonical link, but recent research is enabling the use of non-canonical links like the log link. With the log link, one obtains the so-called log-binomial model which permits the direct estimation of log probabilities and risk ratios. We are exploring here the situations where the estimates of odds ratios and risk ratios from these two models are close and when the estimates are meaningfully different. This provides insight into the choice of link. We extend these results to ordinal outcomes again comparing the logit link and log link.

logit link

log link

logistic regression

log-binomial model

dichotomous outcomes

ordinal outcomes 

Biometrics Section