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I am interested in modeling the probability of default (PD) of a loan product.

Data

  • I have a dataset going back several years. Most of the loans have reached their terminal state (paid off or default) but there is a considerable number that are still active.
  • Each observation represents a loan.
  • The dependent variable represents whether a loan paid off, defaulted, or is active as of the date the dataset was created.
  • There are also variables which I indend to use as explanatory factors.
  • The age of the loan at the time it paid off/defaulted is unavailable

If I model the probability of default using a logistic regression over the entire dataset, how should I treat the currently active loans? Should they be excluded from the training dataset, or modeled as a non-default state?

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    $\begingroup$ Depending on the problem at hand it might be possible to just ignore the active ones. However, in reality it is often the case that this yields models of a bad quality. The area you need to learn about is called “survival analysis”. In particular, there is a way how to turn any Boolean prediction model (RF, logistic regression, ...) into a survival like model (if I understood correctly): see benkuhn.net/survival-trees . You probably should try this or some native models around survival analysis... $\endgroup$ Feb 16, 2020 at 18:38
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    $\begingroup$ Thanks Fabian. I'm familiar with survival analysis, however the problem I have is that the loans in this data were created over the span of decades but I don't have the a time-based variable to estimate a hazard rate. The other wrinkle is that the hazard rate of these loans is hypothesized to have evolved over the years. $\endgroup$
    – MrT
    Feb 16, 2020 at 21:26
  • $\begingroup$ So you don't have the time of origin of the loans? You only know that the loan is active on a given date, not how long it has been active for? There is no hope of obtaining that information? $\endgroup$ Feb 17, 2020 at 1:46
  • $\begingroup$ I have the date of origin, so I can derive how long a loan has been active for. However for loans that have become inactive, I do not have the date at which they became inactive. $\endgroup$
    – MrT
    Feb 17, 2020 at 14:30

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You could refine your question slightly to assess the probability of default by X months after the loan was created. That way, any loans which are still active after X months yield an outcome of 0.

Censored observations only tell you that they have not defaulted yet, and so to properly account for this, you would need to do a Cox regression.

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  • $\begingroup$ The issue is that I do not have data on when a loan defaulted. I can infer the current age of an active loan because I know when it was created. $\endgroup$
    – MrT
    Feb 17, 2020 at 14:34

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