BTYD (version 2.4)

spend.LL: Spend Log-Likelihood

Description

Calculates the log-likelihood of the gamma-gamma model for customer spending.

Usage

spend.LL(params, m.x, x)

Arguments

params

a vector of gamma-gamma parameters: p, q, and gamma, in that order. p is the shape parameter for each transaction. The scale parameter for each transaction is distributed across customers according to a gamma distribution with parameters q (shape) and gamma (scale).

m.x

a customer's average observed transaction value in the calibration period, or a vector of average observed transaction values - see details.

x

the number of transactions a customer made in the calibration period or a vector of frequencies - see details.

Value

The log-likelihood of the gamma-gamma model. If m.x or x has a length greater than 1, this is a vector of log-likelihoods.

Details

m.x and x may be vectors. The standard rules for vector operations apply - if they are not of the same length, the shorter vector will be recycled (start over at the first element) until it is 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 a vector of log-likelihoods.

References

Fader, Peter S., Bruce G.S. Hardie, and Ka L. Lee. “RFM and CLV: Using Iso-Value Curves for Customer Base Analysis.” Journal of Marketing Research Vol.42, pp.415-430. November. 2005. http://www.brucehardie.com/papers.html

Examples

data(cdnowSummary)
ave.spend <- cdnowSummary$m.x;
tot.trans <- cdnowSummary$cbs[,"x"];
params <- c(6.25, 3.74, 15.44);

# get the total log-likelihood of the data and parameters
# above. There will be many warnings due to the zeroes that are
# included in the data. If you wish to avoid these warnings, use:

# ave.spend <- ave.spend[which(tot.trans > 0)];
# and
# tot.trans <- tot.trans[which(tot.trans > 0)];

# Note that we used tot.trans to remove the zeroes from ave.spend.
# This is because we need the vectors to be the same length, and it
# is possible that your data include customers who made transactions
# worth zero dollars (in which case the vector lengths would differ
# if we used ave.spend to remove the zeroes from ave.spend).

sum(spend.LL(params, ave.spend, tot.trans))

# This log-likelihood may be different than mentioned in the
# referenced paper; in the paper, a slightly different function
# which relies on total spend (not average spend) is used.