diagnostic: link test - nonlinearity test for many model

see Stata ‘r.pdf’ manual

estimate y with exog_test = (fittedvalues, fittedvalues**2) reject correct specification if fittedvalues**2 is significant

there might be something similar for OLS already, but Stata’s link test works for discrete models, e.g. after Logit. For example for Logit we have to run a Logit(endog, exog_test).fit(...) again. (do we have all information to run model and fit with the same options again?)

if rejected: either some missing non-linearities in the explanatory variables or incorrectly specified link function

edit don’t use fittedvalues, use predict(linear=True), fittedvalues should be refactored to return the transformed, expected mean or estimated mean function E(y|x).

[josef-pkt]

look at https://github.com/statsmodels/statsmodels/blob/master/statsmodels/stats/outliers_influence.py#L102

Essentially we need the same thing for other models than OLS. The call to OLS needs to be replace by a GLM model. The extra keywords that the user used when creating the model like offset, exposure and weights in the GLM case are available in the _init_kwds attribute. There should be some examples for the creation of a new GLM model in the statsmodels source, but I don’t remember where.

[mina1987]

see Stata ‘r.pdf’ manual

estimate y with exog_test = (fittedvalues, fittedvalues**2) reject correct specification if fittedvalues**2 is significant

there might be something similar for OLS already, but Stata’s link test works for discrete models, e.g. after Logit. For example for Logit we have to run a Logit(endog, exog_test).fit(...) again. (do we have all information to run model and fit with the same options again?)

if rejected: either some missing non-linearities in the explanatory variables or incorrectly specified link function

edit don’t use fittedvalues, use predict(linear=True), fittedvalues should be refactored to return the transformed, expected mean or estimated mean function E(y|x).

I am trying to contribute to this issue but having trouble figuring out what needs to be done. Is it about a linktest for GLM that takes model as an argument?