Probabilistic customer attrition models predict in general three expected characteristics for every customer:

  • "conditional expected transactions" (CET), which is the number of transactions to expect from a customer during the prediction period,

  • "probability of a customer being alive" (PAlive) at the end of the estimation period and

  • "discounted expected residual transactions" (DERT) for every customer, which is the total number of transactions for the residual lifetime of a customer discounted to the end of the estimation period. In the case of time-varying covariates, instead of DERT, "discounted expected conditional transactions" (DECT) is predicted. DECT does only cover a finite time horizon in contrast to DERT. For continuous.discount.factor=0, DECT corresponds to CET.

In order to derive a monetary value such as CLV, customer spending has to be considered. If the clv.data object contains spending information, customer spending can be predicted using a Gamma/Gamma spending model for parameter predict.spending and the predicted CLV is be calculated (if the transaction model supports DERT/DECT). In this case, the prediction additionally contains the following two columns:

  • "predicted.mean.spending", the mean spending per transactions as predicted by the spending model.

  • "CLV", the customer lifetime value. CLV is the product of DERT/DECT and predicted spending.

# S3 method for clv.fitted.transactions
predict(
  object,
  newdata = NULL,
  prediction.end = NULL,
  predict.spending = gg,
  continuous.discount.factor = 0.1,
  verbose = TRUE,
  ...
)

# S4 method for clv.fitted.transactions
predict(
  object,
  newdata = NULL,
  prediction.end = NULL,
  predict.spending = gg,
  continuous.discount.factor = 0.1,
  verbose = TRUE,
  ...
)

Arguments

object

A fitted clv transaction model for which prediction is desired.

newdata

A clv data object for which predictions should be made with the fitted model. If none or NULL is given, predictions are made for the data on which the model was fit.

prediction.end

Until what point in time to predict. This can be the number of periods (numeric) or a form of date/time object. See details.

predict.spending

Whether and how to predict spending and based on it also CLV, if possible. See details.

continuous.discount.factor

continuous discount factor to use to calculate DERT/DECT

verbose

Show details about the running of the function.

...

Ignored

Value

An object of class data.table with columns:

Id

The respective customer identifier

period.first

First timepoint of prediction period

period.last

Last timepoint of prediction period

period.length

Number of time units covered by the period indicated by period.first and period.last (including both ends).

PAlive

Probability to be alive at the end of the estimation period

CET

The Conditional Expected Transactions

DERT or DECT

Discounted Expected Residual Transactions or Discounted Expected Conditional Transactions for dynamic covariates models

actual.x

Actual number of transactions until prediction.end. Only if there is a holdout period and the prediction ends in it, otherwise it is not reported.

actual.total.spending

Actual total spending until prediction.end. Only if there is a holdout period and the prediction ends in it, otherwise it is not reported.

predicted.mean.spending

The mean spending per transactions as predicted by the spending model.

predicted.CLV

Customer Lifetime Value based on DERT/DECT and predicted.mean.spending.

Details

predict.spending indicates whether to predict customers' spending and if so, the spending model to use. Accepted inputs are either a logical (TRUE/FALSE), a method to fit a spending model (i.e. gg), or an already fitted spending model. If provided TRUE, a Gamma-Gamma model is fit with default options. If argument newdata is provided, the spending model is fit on newdata. Predicting spending is only possible if the transaction data contains spending information. See examples for illustrations of valid inputs.

The newdata argument has to be a clv data object of the exact same class as the data object on which the model was fit. In case the model was fit with covariates, newdata needs to contain identically named covariate data.

The use case for newdata is mainly two-fold: First, to estimate model parameters only on a sample of the data and then use the fitted model object to predict or plot for the full data set provided through newdata. Second, for models with dynamic covariates, to provide a clv data object with longer covariates than contained in the data on which the model was estimated what allows to predict or plot further. When providing newdata, some models might require additional steps that can significantly increase runtime.

prediction.end indicates until when to predict or plot and can be given as either a point in time (of class Date, POSIXct, or character) or the number of periods. If prediction.end is of class character, the date/time format set when creating the data object is used for parsing. If prediction.end is the number of periods, the end of the fitting period serves as the reference point from which periods are counted. Only full periods may be specified. If prediction.end is omitted or NULL, it defaults to the end of the holdout period if present and to the end of the estimation period otherwise.

The first prediction period is defined to start right after the end of the estimation period. If for example weekly time units are used and the estimation period ends on Sunday 2019-01-01, then the first day of the first prediction period is Monday 2019-01-02. Each prediction period includes a total of 7 days and the first prediction period therefore will end on, and include, Sunday 2019-01-08. Subsequent prediction periods again start on Mondays and end on Sundays. If prediction.end indicates a timepoint on which to end, this timepoint is included in the prediction period.

continuous.discount.factor allows to adjust the discount rate used to estimated the discounted expected transactions (DERT/DECT). The default value is 0.1 (=10%). Note that a continuous rate needs to be provided.

See also

models to predict transactions: pnbd, bgnbd, ggomnbd.

models to predict spending: gg.

predict for spending models

Examples

# \donttest{ data("apparelTrans") # Fit pnbd standard model on data, WITH holdout apparel.holdout <- clvdata(apparelTrans, time.unit="w", estimation.split=37, date.format="ymd") apparel.pnbd <- pnbd(apparel.holdout)
#> Starting estimation...
#> Estimation finished!
# Predict until the end of the holdout period predict(apparel.pnbd)
#> Predicting from 2005-09-20 until (incl.) 2006-07-16 (42.86 Weeks).
#> Estimating gg model to predict spending...
#> Starting estimation...
#> Estimation finished!
#> Id period.first period.last period.length actual.x actual.total.spending #> 1: 1 2005-09-20 2006-07-16 42.85714 0 0.00 #> 2: 10 2005-09-20 2006-07-16 42.85714 0 0.00 #> 3: 100 2005-09-20 2006-07-16 42.85714 23 737.53 #> 4: 1000 2005-09-20 2006-07-16 42.85714 25 1120.41 #> 5: 1001 2005-09-20 2006-07-16 42.85714 11 364.00 #> --- #> 246: 1219 2005-09-20 2006-07-16 42.85714 14 413.76 #> 247: 122 2005-09-20 2006-07-16 42.85714 0 0.00 #> 248: 1220 2005-09-20 2006-07-16 42.85714 0 0.00 #> 249: 1221 2005-09-20 2006-07-16 42.85714 9 302.65 #> 250: 1222 2005-09-20 2006-07-16 42.85714 0 0.00 #> PAlive CET DERT predicted.mean.spending predicted.CLV #> 1: 0.3909507 0.269518 0.06742987 40.39473 2.723811 #> 2: 0.4683642 1.145548 0.28660121 57.49121 16.477049 #> 3: 0.9858258 16.263678 4.06895942 43.83628 178.368045 #> 4: 0.9948488 12.917715 3.23184305 43.46097 140.459030 #> 5: 0.6492950 5.009457 1.25330058 46.17636 57.872865 #> --- #> 246: 0.9859138 4.143114 1.03655278 33.20726 34.421081 #> 247: 0.3909507 0.269518 0.06742987 40.39473 2.723811 #> 248: 0.3909507 0.269518 0.06742987 40.39473 2.723811 #> 249: 0.9762838 4.960046 1.24093869 34.00868 42.202689 #> 250: 0.4471937 0.701030 0.17538854 48.80122 8.559174
# Predict until 10 periods (weeks in this case) after # the end of the 37 weeks fitting period predict(apparel.pnbd, prediction.end = 10) # ends on 2010-11-28
#> Predicting from 2005-09-20 until (incl.) 2005-11-28 (10 Weeks).
#> Estimating gg model to predict spending...
#> Starting estimation...
#> Estimation finished!
#> Id period.first period.last period.length actual.x actual.total.spending #> 1: 1 2005-09-20 2005-11-28 10 0 0.00 #> 2: 10 2005-09-20 2005-11-28 10 0 0.00 #> 3: 100 2005-09-20 2005-11-28 10 6 134.15 #> 4: 1000 2005-09-20 2005-11-28 10 9 318.20 #> 5: 1001 2005-09-20 2005-11-28 10 3 118.22 #> --- #> 246: 1219 2005-09-20 2005-11-28 10 3 93.92 #> 247: 122 2005-09-20 2005-11-28 10 0 0.00 #> 248: 1220 2005-09-20 2005-11-28 10 0 0.00 #> 249: 1221 2005-09-20 2005-11-28 10 4 91.80 #> 250: 1222 2005-09-20 2005-11-28 10 0 0.00 #> PAlive CET DERT predicted.mean.spending predicted.CLV #> 1: 0.3909507 0.06948088 0.06742987 40.39473 2.723811 #> 2: 0.4683642 0.29531878 0.28660121 57.49121 16.477049 #> 3: 0.9858258 4.19272526 4.06895942 43.83628 178.368045 #> 4: 0.9948488 3.33014626 3.23184305 43.46097 140.459030 #> 5: 0.6492950 1.29142232 1.25330058 46.17636 57.872865 #> --- #> 246: 0.9859138 1.06808168 1.03655278 33.20726 34.421081 #> 247: 0.3909507 0.06948088 0.06742987 40.39473 2.723811 #> 248: 0.3909507 0.06948088 0.06742987 40.39473 2.723811 #> 249: 0.9762838 1.27868441 1.24093869 34.00868 42.202689 #> 250: 0.4471937 0.18072335 0.17538854 48.80122 8.559174
# Predict until 31th Dec 2016 with the timepoint as a character predict(apparel.pnbd, prediction.end = "2016-12-31")
#> Predicting from 2005-09-20 until (incl.) 2016-12-31 (588.71 Weeks).
#> Estimating gg model to predict spending...
#> Starting estimation...
#> Estimation finished!
#> Id period.first period.last period.length PAlive CET #> 1: 1 2005-09-20 2016-12-31 588.7143 0.3909507 2.095867 #> 2: 10 2005-09-20 2016-12-31 588.7143 0.4683642 8.908191 #> 3: 100 2005-09-20 2016-12-31 588.7143 0.9858258 126.472146 #> 4: 1000 2005-09-20 2016-12-31 588.7143 0.9948488 100.452740 #> 5: 1001 2005-09-20 2016-12-31 588.7143 0.6492950 38.955319 #> --- #> 246: 1219 2005-09-20 2016-12-31 588.7143 0.9859138 32.218324 #> 247: 122 2005-09-20 2016-12-31 588.7143 0.3909507 2.095867 #> 248: 1220 2005-09-20 2016-12-31 588.7143 0.3909507 2.095867 #> 249: 1221 2005-09-20 2016-12-31 588.7143 0.9762838 38.571085 #> 250: 1222 2005-09-20 2016-12-31 588.7143 0.4471937 5.451459 #> DERT predicted.mean.spending predicted.CLV #> 1: 0.06742987 40.39473 2.723811 #> 2: 0.28660121 57.49121 16.477049 #> 3: 4.06895942 43.83628 178.368045 #> 4: 3.23184305 43.46097 140.459030 #> 5: 1.25330058 46.17636 57.872865 #> --- #> 246: 1.03655278 33.20726 34.421081 #> 247: 0.06742987 40.39473 2.723811 #> 248: 0.06742987 40.39473 2.723811 #> 249: 1.24093869 34.00868 42.202689 #> 250: 0.17538854 48.80122 8.559174
# Predict until 31th Dec 2016 with the timepoint as a Date predict(apparel.pnbd, prediction.end = lubridate::ymd("2016-12-31"))
#> Predicting from 2005-09-20 until (incl.) 2016-12-31 (588.71 Weeks).
#> Estimating gg model to predict spending...
#> Starting estimation...
#> Estimation finished!
#> Id period.first period.last period.length PAlive CET #> 1: 1 2005-09-20 2016-12-31 588.7143 0.3909507 2.095867 #> 2: 10 2005-09-20 2016-12-31 588.7143 0.4683642 8.908191 #> 3: 100 2005-09-20 2016-12-31 588.7143 0.9858258 126.472146 #> 4: 1000 2005-09-20 2016-12-31 588.7143 0.9948488 100.452740 #> 5: 1001 2005-09-20 2016-12-31 588.7143 0.6492950 38.955319 #> --- #> 246: 1219 2005-09-20 2016-12-31 588.7143 0.9859138 32.218324 #> 247: 122 2005-09-20 2016-12-31 588.7143 0.3909507 2.095867 #> 248: 1220 2005-09-20 2016-12-31 588.7143 0.3909507 2.095867 #> 249: 1221 2005-09-20 2016-12-31 588.7143 0.9762838 38.571085 #> 250: 1222 2005-09-20 2016-12-31 588.7143 0.4471937 5.451459 #> DERT predicted.mean.spending predicted.CLV #> 1: 0.06742987 40.39473 2.723811 #> 2: 0.28660121 57.49121 16.477049 #> 3: 4.06895942 43.83628 178.368045 #> 4: 3.23184305 43.46097 140.459030 #> 5: 1.25330058 46.17636 57.872865 #> --- #> 246: 1.03655278 33.20726 34.421081 #> 247: 0.06742987 40.39473 2.723811 #> 248: 0.06742987 40.39473 2.723811 #> 249: 1.24093869 34.00868 42.202689 #> 250: 0.17538854 48.80122 8.559174
# Predict future transactions but not spending and CLV predict(apparel.pnbd, predict.spending = FALSE)
#> Predicting from 2005-09-20 until (incl.) 2006-07-16 (42.86 Weeks).
#> Id period.first period.last period.length actual.x actual.total.spending #> 1: 1 2005-09-20 2006-07-16 42.85714 0 0.00 #> 2: 10 2005-09-20 2006-07-16 42.85714 0 0.00 #> 3: 100 2005-09-20 2006-07-16 42.85714 23 737.53 #> 4: 1000 2005-09-20 2006-07-16 42.85714 25 1120.41 #> 5: 1001 2005-09-20 2006-07-16 42.85714 11 364.00 #> --- #> 246: 1219 2005-09-20 2006-07-16 42.85714 14 413.76 #> 247: 122 2005-09-20 2006-07-16 42.85714 0 0.00 #> 248: 1220 2005-09-20 2006-07-16 42.85714 0 0.00 #> 249: 1221 2005-09-20 2006-07-16 42.85714 9 302.65 #> 250: 1222 2005-09-20 2006-07-16 42.85714 0 0.00 #> PAlive CET DERT #> 1: 0.3909507 0.269518 0.06742987 #> 2: 0.4683642 1.145548 0.28660121 #> 3: 0.9858258 16.263678 4.06895942 #> 4: 0.9948488 12.917715 3.23184305 #> 5: 0.6492950 5.009457 1.25330058 #> --- #> 246: 0.9859138 4.143114 1.03655278 #> 247: 0.3909507 0.269518 0.06742987 #> 248: 0.3909507 0.269518 0.06742987 #> 249: 0.9762838 4.960046 1.24093869 #> 250: 0.4471937 0.701030 0.17538854
# Predict spending by fitting a Gamma-Gamma model predict(apparel.pnbd, predict.spending = gg)
#> Predicting from 2005-09-20 until (incl.) 2006-07-16 (42.86 Weeks).
#> Estimating gg model to predict spending...
#> Starting estimation...
#> Estimation finished!
#> Id period.first period.last period.length actual.x actual.total.spending #> 1: 1 2005-09-20 2006-07-16 42.85714 0 0.00 #> 2: 10 2005-09-20 2006-07-16 42.85714 0 0.00 #> 3: 100 2005-09-20 2006-07-16 42.85714 23 737.53 #> 4: 1000 2005-09-20 2006-07-16 42.85714 25 1120.41 #> 5: 1001 2005-09-20 2006-07-16 42.85714 11 364.00 #> --- #> 246: 1219 2005-09-20 2006-07-16 42.85714 14 413.76 #> 247: 122 2005-09-20 2006-07-16 42.85714 0 0.00 #> 248: 1220 2005-09-20 2006-07-16 42.85714 0 0.00 #> 249: 1221 2005-09-20 2006-07-16 42.85714 9 302.65 #> 250: 1222 2005-09-20 2006-07-16 42.85714 0 0.00 #> PAlive CET DERT predicted.mean.spending predicted.CLV #> 1: 0.3909507 0.269518 0.06742987 40.39473 2.723811 #> 2: 0.4683642 1.145548 0.28660121 57.49121 16.477049 #> 3: 0.9858258 16.263678 4.06895942 43.83628 178.368045 #> 4: 0.9948488 12.917715 3.23184305 43.46097 140.459030 #> 5: 0.6492950 5.009457 1.25330058 46.17636 57.872865 #> --- #> 246: 0.9859138 4.143114 1.03655278 33.20726 34.421081 #> 247: 0.3909507 0.269518 0.06742987 40.39473 2.723811 #> 248: 0.3909507 0.269518 0.06742987 40.39473 2.723811 #> 249: 0.9762838 4.960046 1.24093869 34.00868 42.202689 #> 250: 0.4471937 0.701030 0.17538854 48.80122 8.559174
# Fit a spending model separately and use it to predict spending apparel.gg <- gg(apparel.holdout, remove.first.transaction = FALSE)
#> Starting estimation...
#> Estimation finished!
predict(apparel.pnbd, predict.spending = apparel.gg)
#> Predicting from 2005-09-20 until (incl.) 2006-07-16 (42.86 Weeks).
#> Id period.first period.last period.length actual.x actual.total.spending #> 1: 1 2005-09-20 2006-07-16 42.85714 0 0.00 #> 2: 10 2005-09-20 2006-07-16 42.85714 0 0.00 #> 3: 100 2005-09-20 2006-07-16 42.85714 23 737.53 #> 4: 1000 2005-09-20 2006-07-16 42.85714 25 1120.41 #> 5: 1001 2005-09-20 2006-07-16 42.85714 11 364.00 #> --- #> 246: 1219 2005-09-20 2006-07-16 42.85714 14 413.76 #> 247: 122 2005-09-20 2006-07-16 42.85714 0 0.00 #> 248: 1220 2005-09-20 2006-07-16 42.85714 0 0.00 #> 249: 1221 2005-09-20 2006-07-16 42.85714 9 302.65 #> 250: 1222 2005-09-20 2006-07-16 42.85714 0 0.00 #> PAlive CET DERT predicted.mean.spending predicted.CLV #> 1: 0.3909507 0.269518 0.06742987 70.27718 4.738781 #> 2: 0.4683642 1.145548 0.28660121 61.78767 17.708422 #> 3: 0.9858258 16.263678 4.06895942 42.33307 172.251543 #> 4: 0.9948488 12.917715 3.23184305 41.93464 135.526187 #> 5: 0.6492950 5.009457 1.25330058 45.28636 56.757418 #> --- #> 246: 0.9859138 4.143114 1.03655278 29.90681 30.999985 #> 247: 0.3909507 0.269518 0.06742987 34.95251 2.356843 #> 248: 0.3909507 0.269518 0.06742987 37.82832 2.550759 #> 249: 0.9762838 4.960046 1.24093869 30.88611 38.327763 #> 250: 0.4471937 0.701030 0.17538854 48.29395 8.470205
# Fit pnbd standard model WITHOUT holdout pnc <- pnbd(clvdata(apparelTrans, time.unit="w", date.format="ymd"))
#> Starting estimation...
#> Estimation finished!
# This fails, because without holdout, a prediction.end is required if (FALSE) { predict(pnc) } # But it works if providing a prediction.end predict(pnc, prediction.end = 10) # ends on 2016-12-17
#> Predicting from 2006-07-17 until (incl.) 2006-09-24 (10 Weeks).
#> Estimating gg model to predict spending...
#> Starting estimation...
#> Estimation finished!
#> Id period.first period.last period.length PAlive CET #> 1: 1 2006-07-17 2006-09-24 10 0.19163346 0.01673295 #> 2: 10 2006-07-17 2006-09-24 10 0.07060649 0.02243407 #> 3: 100 2006-07-17 2006-09-24 10 0.99543392 4.78888517 #> 4: 1000 2006-07-17 2006-09-24 10 0.99921327 4.57683199 #> 5: 1001 2006-07-17 2006-09-24 10 0.92654506 2.10906899 #> --- #> 246: 1219 2006-07-17 2006-09-24 10 0.80938690 1.74913714 #> 247: 122 2006-07-17 2006-09-24 10 0.19163346 0.01673295 #> 248: 1220 2006-07-17 2006-09-24 10 0.19163346 0.01673295 #> 249: 1221 2006-07-17 2006-09-24 10 0.88302134 1.50134084 #> 250: 1222 2006-07-17 2006-09-24 10 0.12412318 0.02513813 #> DERT predicted.mean.spending predicted.CLV #> 1: 0.01636655 38.64708 0.6325194 #> 2: 0.02194282 50.23072 1.1022038 #> 3: 4.68402219 37.91699 177.6040339 #> 4: 4.47661237 43.53497 194.8891854 #> 5: 2.06288637 39.80794 82.1192635 #> --- #> 246: 1.71083601 31.80966 54.4211122 #> 247: 0.01636655 38.64708 0.6325194 #> 248: 0.01636655 38.64708 0.6325194 #> 249: 1.46846574 34.22209 50.2539634 #> 250: 0.02458767 44.10134 1.0843494
# }