# Are there any reasons to use the identity link in logistic regression (or any other glm)?

From this answer, the following statement is posed: 'Though not "wrong", you'd want a good reason for using an identity link to model a Bernoulli probability.'

I would like to know what good reasons would result in an identity link being used for logistic regression, if these exist. Do these reasons generalise to GLMs?

I frequently use the identity link to model a Bernoulli probability when I want to obtain adjusted risk differences or just an adjusted risk. If you wanted to obtain risk differences (e.g. $\hat{p_1}-\hat{p_2}$), and have no need to calculate odds ratios, this is the most straight forward way to calculate them. See this paper for additional details: http://aje.oxfordjournals.org/content/162/3/199.full
• @Alex, how would you get a negative probability? In logistic regression, $\hat{p}$ is restricted to be between 0 and 1. Feb 25 '16 at 17:36
• Hi, @Alex, sorry, I misunderstand your previous reference to $\hat{p}$ -- I thought you were using in the logistic regression context with a logit link. Yes, using an identity link, you can indeed obtain risks that fall outside of 0 and 1 and the models can sometimes fail to converge. There have been methods proposed on how to handle a situation when that occurs. Feb 25 '16 at 23:46