Abstract
Current opinion regarding the selection of link function in binary response models
is that the probit and logit links give essentially similar results. This seems to be true for univariate
binary response models; however, for multivariate binary response models such advice
is misleading. We address a gap in the literature by empirically examining the relationship
between link function selection and model fit in two classes of multivariate binary response
models. We find clear evidence that model fit can be improved by the selection of the appropriate
link even in small data sets. In multivariate link function models, the logit link provides
better fit in the presence of extreme independent variable levels. Conversely, model fit in random
effects models with moderate size data sets is improved generally by selecting the probit
link.
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