Solved – R binomial family with identity link

Question

I want to fit a linear model by R with family=binomial(link="identity"), however, binomial family do not have identity link. What should I do?

Answer 1

See Wikipedia on the linear probability model, & CV posts here & here for the statistical background. Though not "wrong", you'd want a good reason for using an identity link to model a Bernoulli probability.

According to the family manual

the binomial family [accepts] the links logit, probit, cauchit, (corresponding to logistic, normal and Cauchy CDFs respectively) log and cloglog (complementary log-log)

But

The link and variance arguments have rather awkward semantics for back-compatibility. The recommended way is to supply them is as quoted character strings, but they can also be supplied unquoted (as names or expressions). In addition, they can also be supplied as a length-one character vector giving the name of one of the options, or as a list (for link, of class "link-glm"). The restrictions apply only to links given as names: when given as a character string all the links known to make.link are accepted.

So family=binomial(link="identity") works but family=binomial(link=identity) doesn't. (If you find differently it might be to do with the R version.) To allow for over-dispersion, then usefamily=quasi(link="identity", variance = "mu(1-mu)").