BTYD (version 2.4)

bgbb.LL: BG/BB Log-Likelihood

Description

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

Usage

bgbb.rf.matrix.LL(params, rf.matrix)
bgbb.LL(params, x, t.x, n.cal)

Arguments

params

BG/BB parameters - a vector with alpha, beta, gamma, and delta, in that order. Alpha and beta are unobserved parameters for the beta-Bernoulli transaction process. Gamma and delta are unobserved parameters for the beta-geometric dropout process.

rf.matrix

recency-frequency matrix. It must contain columns for frequency ("x"), recency ("t.x"), number of transaction opportunities in the calibration period ("n.cal"), and the number of customers with this combination of recency, frequency and transaction opportunities in the calibration period ("custs"). 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.

x

the number of repeat transactions made by the customer in the calibration period. Can also be vector of frequencies - see details.

t.x

recency - the transaction opportunity in which the customer made their last transaction. Can also be a vector of recencies - see details.

n.cal

number of transaction opportunities in the calibration period. Can also be a vector of calibration period transaction opportunities - see details.

Value

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

Details

x, t.x, and n.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.

References

Fader, Peter S., Bruce G.S. Hardie, and Jen Shang. “Customer-Base Analysis in a Discrete-Time Noncontractual Setting.” Marketing Science 29(6), pp. 1086-1108. 2010. INFORMS. http://www.brucehardie.com/papers/020/

Examples

data(donationsSummary)

rf.matrix <- donationsSummary$rf.matrix
# donationsSummary$rf.matrix already has appropriate column names

params <- c(1.20, 0.75, 0.66, 2.78)
bgbb.rf.matrix.LL(params, rf.matrix)

# Returns the log likelihood of the parameters for a customer who
# made 3 transactions in a calibration period with 6 transaction opportunities,
# with the last transaction occurring during the 4th transaction opportunity.
bgbb.LL(params, x=3, t.x=4, n.cal=6)

# We can also give vectors as function parameters:
set.seed(7)
x <- sample(1:3, 10, replace = TRUE)
t.x <- sample(3:5, 10, replace = TRUE)
n.cal <- rep(5, 10)
bgbb.LL(params, x, t.x, n.cal)