I am following up from my question here. As described there, I'm trying to assess the drivers of CPRs for a type of MBS. However, I want to understand, how a loan-level model of such a relationship would look? Specifically, how does one model the drivers of prepayment at the loan level, as a typical regression will not work given that the data is both longitudinal and cross-sectional in nature. So, in this case, is there a tried and tested regression or other procedure that is used? I am leaning towards a Fixed Effect model.
Probably the most established (thus far...) academic approach to this problem is to use a multinomial logistic regression (the search terms "prepayment model multinomial logit" should turn up dozens of papers). Longitudinal effects are captured in some of these models by including time-dependent explanatory variables such as an index that captures the availability of mortgage credit, the vintage of a loan etc.
On the other hand, it is not clear that prepayment data satisfies a crucial assumption made by the model, namely the "independence of irrelevant alternatives." Various extensions have been proposed to the baseline MNL framework to handle this but these introduce additional layers of complexity to the estimation process.
Unfortunately, there is no canonical reference (that I know of) that provides a guided tour through these nuances in the context of prepayment modeling. Going through the modeling details of some of the papers found by searching and working through their references and also asking specific questions appears to be the only way right now.