pnbd.EstimateParameters {BTYD}

Pareto/NBD Parameter Estimation

Description

The best-fitting parameters are determined using the pnbd.cbs.LL function. The sum of the log-likelihood for each customer (for a set of parameters) is maximized in order to estimate parameters.

Usage

pnbd.EstimateParameters(
  cal.cbs,
  par.start = c(1, 1, 1, 1),
  max.param.value = 10000,
  method = "L-BFGS-B",
  hardie = TRUE,
  hessian = FALSE
)

Arguments

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 labelled "custs" (number of customers with a specific combination of recency, frequency and length of calibration period) will make this function faster.

par.start

initial Pareto/NBD parameters - a vector with r, alpha, s, and beta, in that order. r and alpha are unobserved parameters for the NBD transaction process. s and beta are unobserved parameters for the Pareto (exponential gamma) dropout process.

max.param.value

the upper bound on parameters.

method

the optimization method(s).

hardie

if TRUE, have pnbd.LL use h2f1 instead of hypergeo.

hessian

set it to TRUE if you want the Hessian matrix, and then you might as well have the complete optimx object returned.

Details

A set of starting parameters must be provided for this method. If no parameters are provided, (1,1,1,1) is used as a default. It may be useful to use starting values for r and s that represent your best guess of the heterogeneity in the buy and die rate of customers. It may be necessary to run the estimation from multiple starting points to ensure that it converges. To compare the log-likelihoods of different parameters, use pnbd.cbs.LL.

The lower bound on the parameters to be estimated is always zero, since Pareto/NBD parameters cannot be negative. The upper bound can be set with the max.param.value parameter.

This function may take some time to run. It uses optimx for maximum likelihood estimation, not optim.

Value

Unnamed vector of estimated parameters by default, optimx object with everything if hessian is TRUE.

References

Fader, Peter S.; Hardie, and Bruce G.S.. "Overcoming the BG/NBD Model's #NUM! Error Problem." December. 2013. Web. http://brucehardie.com/notes/027/bgnbd_num_error.pdf

See Also

pnbd.cbs.LL

Examples

data(cdnowSummary)

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

# starting-point parameters
startingparams <- c(0.5, 6, 0.9, 8)

# estimated parameters
est.params <- pnbd.EstimateParameters(cal.cbs = cal.cbs, 
                                      par.start = startingparams, 
                                      method = 'L-BFGS-B',
                                      hardie = TRUE)
                                      
# complete object returned by \code{\link[optimx]{optimx}}
optimx.set <- pnbd.EstimateParameters(cal.cbs = cal.cbs, 
                                      par.start = startingparams, 
                                      hardie = TRUE, 
                                      hessian = TRUE)

# log-likelihood of estimated parameters
pnbd.cbs.LL(est.params, cal.cbs, TRUE)