Evaluating the Choice of Link Function

Often, there will not be a clear theoretical choice of link function based on the data. In cases where the initial model performs poorly, it is usually worth trying alternative link functions to see if a better model can be constructed with a different link function. Although some of the link functions perform quite similarly in many instances (particularly the logit, complementary log-log and negative log-log functions), there are situations where choice of link function can make or break your model.

In this example, there are at least two link functions (complementary log-log and Cauchit) that may be appropriate. Although the model does fairly well with the complementary log-log link, it might be possible to improve the model fit by using the Cauchit link function.

You can now estimate a new model with a Cauchit link function to see whether the change increases the predictive utility of the model. It is recommended to keep the same set of predictor variables in the model until you have finished evaluating link functions. If you change the link function and the set of predictors at the same time, you won't know which of them caused any change in model fit.

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