I have been using the linktest command after GLM models quite
frequently, and I came to wonder whether it is implemented correctly or
not.
My understanding of the linktest is this:
The linktest uses predictions and the square of the predictions to then
predict the observed variables in a regression that uses the same
specification (distribution and link function) as the original model. So
if the predictions themselves and the squared predictions are included,
the squared predictions should not be significant in their relationship
to the observed variable or a misspecification is indicated.
Now, the linktest implemented in Stata uses
predict, xb
As the default to generate the predictions for the link test. In case of
GLM models with non-identity-link-functions this means that the
predictions are not in the same scale as the observed variable but
rather the untransformed, linear combination generated by the model. So
if you would use those predictions based on, for example, an inverse
link function, there is no real reason to believe that those are a
straight-forward predictor of the observed variables even if no
non-linear term is included in link-test-regression, especially because
re-running the models with the inverted predictions would then again
apply the same link-functions to those predicted values.
Does anyone have experience with this? Is it possible that the revision
of GLM models for the more recent stata version has changed some of the
meaning of predictions and is not correctly implemented in the linktest
command that seems to be based on an older Stata version?
Any help with this issue is greatly appreciated...
Daniel Schneider
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