BTYD (version 2.4)

bgbb.PlotTrackingCum: BG/BB Tracking Cumulative Transactions Plot

Description

Plots the actual and expected cumulative total repeat transactions by all customers for the calibration and holdout periods. Also returns a matrix with this comparison.

Usage

bgbb.PlotTrackingCum(params, rf.matrix, actual.cum.repeat.transactions, xlab = "Time", ylab = "Cumulative Transactions", xticklab = NULL, title = "Tracking Cumulative Transactions")

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 the number of transactions opportunities in the calibration period ("n.cal"), and the number of customers with this number of transaction opportunities in the calibration period ("custs"). Columns for frequency and recency may be in the matrix, but are not necessary for this function since it relies on bgbb.Expectation, which only requires the number of transaction opportunities.

actual.cum.repeat.transactions

vector containing the cumulative number of repeat transactions made by customers in all transaction opportunities (both calibration and holdout periods). Its unit of time should be the same as the units of the recency-frequency matrix used to estimate the model parameters.

xlab

descriptive label for the x axis.

ylab

descriptive label for the y axis.

xticklab

vector containing a label for each tick mark on the x axis.

title

title placed on the top-center of the plot.

Value

Matrix containing actual and expected cumulative repeat transactions.

Details

The holdout period should immediately follow the calibration period. This function assumes that all customers' calibration periods end on the same date, rather than starting on the same date (thus customers' birth periods are determined using max(n.cal) - n.cal rather than assuming that it is 0).

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

# starting-point parameters
startingparams <- c(1, 1, 0.5, 3)
# estimated parameters
est.params <- bgbb.EstimateParameters(rf.matrix, startingparams)

# get the annual repeat transactions, and transform them into
# a cumulative form
actual.inc.repeat.transactions <- donationsSummary$annual.trans
actual.cum.repeat.transactions <- cumsum(actual.inc.repeat.transactions)

# set appropriate x-axis
x.tickmarks <- c( "'96","'97","'98","'99","'00","'01","'02","'03","'04","'05","'06" )

# plot actual vs. expected transactions. The calibration period was 6 periods long.
bgbb.PlotTrackingCum(est.params, rf.matrix, actual.cum.repeat.transactions, xticklab=x.tickmarks)