# BTYD R package. Why dropping the first puchase in the BG/NBD model?

I am using the BTYD package on R to estimate the probability of a customer churning after my calibration period. At the moment, I have been following the walkthrough provided on the web which you could find here: https://cran.r-project.org/web/packages/BTYD/vignettes/BTYD-walkthrough.pdf. I have also been working with the newly released package CLVTools which basically does the same as the BTYD package.

My question is regarding a specific point in both packages I do not understand in the BG/NBD model. On page 17 of the walkthrough, it is written the following :

The final cleanup step is a very important one. In the calibration period, the BG/NBD model is generally concerned with repeat transactions—that is, the first transaction is ignored. This is convenient for firms using the model in practice, since it is easier to keep track of all customers who have made at least one transaction (as opposed to trying to account for those who have not made any transactions at all)

Despite this sentence, I do not understand the logic why we should drop the first transaction. But more importantly, the probability of being alive, which you can calculate with the bgnbd.PAlive function provided in the BTYD package always gives 1 for customers who have made a single transaction in the past (calibration period). That looks wrong to me, or at least I do not understand it.

I have been exploring the package with the dataset "apparelTrans" provided in the CLVTools package and my calibration period is the 40 first weeks. With this setup, customer 1 (Id==1) has a probability of being alive of 1 at the end of the calibration period despite the fact that he made one single purchase at the very beginning of the calibration period (I would expect a higher probability of churning). I have compared the BTYD and the CLVTools package and both give the same results, which hints I am missing something.

Would someone be kind enough to explain to me why we drop the first purchase in this model and why the probability of being alive is always 1 for customers who made one purchase only?

Any help would be really appreciated

## 2 Answers

The BG/NBD model assumes that all customers are active at the beginning of the observation period and that a customer can only drop out immediately following a transaction. See section 3 of this paper for details: http://brucehardie.com/papers/018/fader_et_al_mksc_05.pdf. Customers with no repeat transactions during the observation period haven't had a chance to drop out so their probability of being alive equals 1. In essence, the model can't determine if those customers without any repeat transactions have "died" or if their shopping behaviors are such that they make very infrequent purchases.

this is old but I thought I'd leave the information here in case someone else bumps into it while searching. You could use the modified BG/NBD, which does account for the possibility that customers can drop out (never purchase again) after the first purchase

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