bgnbd.cbs.LL {BTYD}

BG/NBD Log-Likelihood Wrapper

Description

Calculates the log-likelihood sum of the BG/NBD model.

Usage

bgnbd.cbs.LL(params, cal.cbs)

Arguments

params

BG/NBD parameters - a vector with r, alpha, a, and b, in that order. r and alpha are unobserved parameters for the NBD transaction process. a and b are unobserved parameters for the Beta geometric dropout process.

cal.cbs

calibration period CBS (customer by sufficient statistic). It must contain columns for frequency ("x"), recency ("t.x"), and total time observed ("T.cal"). Note that recency must be the time between the start of the calibration period and the customer's last transaction, not the time between the customer's last transaction and the end of the calibration period. If your data is compressed (see dc.compress.cbs), a fourth column labeled "custs" (number of customers with a specific combination of recency, frequency and length of calibration period) is available.

Details

Note: do not use a compressed cal.cbs matrix. It makes quicker work for Pareto/NBD estimation as implemented in this package, but the opposite is true for BG/NBD. For proof, compare the definition of the bgnbd.cbs.LL to that of pnbd.cbs.LL.

Value

The total log-likelihood of the provided data.

See Also

bgnbd.EstimateParameters

bgnbd.LL

Examples

data(cdnowSummary)

cal.cbs <- cdnowSummary$cbs
# cal.cbs already has column names required by method

# random assignment of parameters
params <- c(0.5, 6, 1.2, 3.3)
# returns the log-likelihood of the given parameters
bgnbd.cbs.LL(params, cal.cbs)

# compare the speed and results to the following:
cal.cbs.compressed <- dc.compress.cbs(cal.cbs)
bgnbd.cbs.LL (params, cal.cbs.compressed)

# Returns the log likelihood of the parameters for a customer who
# made 3 transactions in a calibration period that ended at t=6,
# with the last transaction occurring at t=4.
bgnbd.LL(params, x=3, t.x=4, T.cal=6)

# We can also give vectors as function parameters:
set.seed(7)
x <- sample(1:4, 10, replace = TRUE)
t.x <- sample(1:4, 10, replace = TRUE)
T.cal <- rep(4, 10)
bgnbd.LL(params, x, t.x, T.cal)