BG/NBD Log-Likelihood

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Description

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

Usage

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

bgnbd.LL(params, x, t.x, T.cal)

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 bgnbd.compress.cbs), a fourth column labelled "custs" (number of customers with a specific combination of recency, frequency and length of calibration period) is available.

x

number of repeat transactions in the calibration period T.cal, or a vector of transaction frequencies.

t.x

time of most recent repeat transaction, or a vector of recencies.

T.cal

length of calibration period, or a vector of calibration period lengths.

Details

x, t.x, T.cal may be vectors. The standard rules for vector operations apply - if they are not of the same length, shorter vectors will be recycled (start over at the first element) until they are as long as the longest vector. It is advisable to keep vectors to the same length and to use single values for parameters that are to be the same for all calculations. If one of these parameters has a length greater than one, the output will be also be a vector.

Value

For bgnbd.cbs.LL, the total log-likelihood of the provided data. For bgnbd.LL, a vector of log-likelihoods as long as the longest input vector (x, t.x, or T.cal).

See Also

bgnbd.EstimateParameters

Examples

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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 <- bgnbd.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)

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