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This is the problem i am trying to solve for a client , and would appreciate some help :

1) I am trying to predict the "time to default" (along with the associated probability for a particular loan to default in month1 , month2..etc.) within a six month time period for a set of retail loans.

2) The independent variables are loan characteristics (time-invariant) which will be observed over a period of 12 months prior to default e.g. loan amount , tenure , repayment history etc.

3) The nature of the data is such that the dependant variable (time to default) is observed only in discrete units i.e. 1 month , 2 months , 3 months etc.

After going through some of the available literature regarding survival analysis , I would prefer to use a suitable parametric method e.g. LIFEREG (after determining the appropriate underlying distribution), firstly because the methodology/results are easy to interpret and explain and secondly because prediction (for future loans) and validation appear to be simpler compared to proportional hazard methods.

So my question , what would be the best way to use parametric methods while allowing for discrete time independent variables as above ?

Thanks :)

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  • $\begingroup$ How do you define default? If it is say 3 months non payment, say, then I would expect it might be better to predict 1month in arrears(using all indep vars), and then a Markov model of in arrears state $\endgroup$ – seanv507 May 26 '15 at 23:44
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If you are really worried about the discrete nature of your observations, you can treat it as interval censored; i.e. if they did not default at 13 months but did by 44, then you record default as having occurred between (13,14). However, if all your intervals are equally spaced, non-overlapping and relatively short, the results you will get are going to be almost identical to just using midpoint imputation; replacing (13,14) with 13.5 won't have a huge impact on your fit. In fact, if you use a semi-parametric model, the results should basically be identical.

You certainly can use parametric regression models for survival analysis: probably the easiest to interpret is the AFT (accelerated failure time) model: the covariates affect how much quicker one group experiences an event compared to another group. This is much easier to understand than, say, proportional hazards. Alternatively, if you are looking at probability of default after one year, a proportional odds model will lead to a very nice interpretation (i.e. the odds this group will default in 12 months is twice as high as this other group).

However, I think using simple parametric regression models is over simplifying things! If a subject pays off their debt, they will never default. I would assume this happens quite often. Because of this, a cure rate model makes much more sense, and simple parametric models will likely be very biased. With this type of data, I would be much more concerned with this than the interval censored nature of the data.

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