I don't think there is the 'best' model. But that which model best fits which research question of yours and and what data you are using. Spoken, written, visual, multimodal, etc. Additionally, there are various approaches to identity, narrative, CA, pragmatics, sociolinguistics, and so on. So you may have to find/create a model for your own research question.
as usual, it depends what kind of identity in what context you would like to study - from matters of personal identity formation over group conflicts to national identity etc.
I suppose you mean 'critical discourse analysis' in the explicit, narrow sense, so you could look for benchmark studies in this field in order to get an impression of adoptable approaches. A first start could also be to search eminent books in this special field, for example the widely used Introduction by Norman Fairclough on 'Critical Discourse Analysis' where questions of identity are also touched (see link below).
There is a very good model which I used in one of my papers. It was proposed by Prof. Reem Bassiouney (2012). It uses a number of discoursal and structural tools to analyze the identity of the speaker or how the speaker is trying to establish the identity of another party.
Bassiouney, R. (2012). Politicizing identity: Code choice and stance-taking during the Egyptian revolution. Discourse & Society, 23 (2), 107-126. Retrieved from http://journals.sagepub.com/doi/abs/10.1177/0957926511431514