Alternate link functions that impose bounds on the input of their link function
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input values less than the cutpoint are replaces with the
cutpoint. For all be
When using survival psuedovalues for binomial regression, the raw data can be
outside the range (0,1), yet we want to restrict the predicted values
to lie within that range. A natural way to deal with this is to use
family = gaussian(link= "logit").
But this will fail.
The reason is that the
family object has a component
linkfun that does not accept values outside of (0,1).
This function is only used to create initial values for the iteration
step, however. Mapping the offending input argument into the range
of (egde, 1-edge) before computing the link results in starting
estimates that are good enough. The final result of the fit will be
no different than if explicit starting estimates were given using the
These functions create copies of the logit, probit, and complimentary
log-log families that differ from the standard ones only in this
use of a bounded input argument, and are called a "bounded logit" =
The same argument hold when using RMST (area under the curve) pseudovalues along with a log link to ensure positive predictions, though in this case only the lower boundary needs to be mapped.
family object of the same form as
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