Fitting of GLM with statsmodels

Question

Python's statsmodels module offers a set of methods to estimate GLM as illustrated in https://www.statsmodels.org/devel/examples/notebooks/generated/glm.html

e.g.

glm_binom = sm.GLM(data.endog, data.exog, family=sm.families.Binomial())

What is the link function in above example? Is it logit link? How can I use other link like loglog?

I tried below without any success

glm_binom = sm.GLM(data.endog, data.exog, family=sm.families.Binomial(link = 'loglog'))

Any pointer will be very helpful

Answer 1

In the latest statsmodels stable release (currently v0.13.2), only the following link functions are available for each sm.families.family:

Family	ident	log	logit	probit	cloglog	pow	opow	nbinom	loglog	logc
Gaussian	X	X	X	X	X	X	X	X	X
Inv Gaussian	X	X				X
Binomial	X	X	X	X	X	X	X		X	X
Poisson	X	X				X
Neg Binomial	X	X				X		X
Gamma	X	X				X
Tweedie	X	X				X

Alternatively, the list of available link functions can be obtained by:

sm.families.family.<familyname>.links

Lastly, in order to change the default link function of the GLM in statsmodels you need to specify the link parameter in the family parameter:

sm.GLM(y, X, family=sm.families.Binomial(link=sm.families.links.loglog()))

P.S. The default link for the Binomial family is the logit link.