gg: Gamma/Gamma Spending model

In CLVTools: Tools for Customer Lifetime Value Estimation

Gamma/Gamma Spending model

Description

Fits the Gamma-Gamma model on a given object of class clv.data to predict customers' mean spending per transaction.

Usage

## S4 method for signature 'clv.data'
gg(
  clv.data,
  start.params.model = c(),
  remove.first.transaction = TRUE,
  optimx.args = list(),
  verbose = TRUE,
  ...
)

Arguments

clv.data	The data object on which the model is fitted.
start.params.model	Named start parameters containing the optimization start parameters for the model without covariates.
remove.first.transaction	Whether customer's first transaction are removed. If TRUE all zero-repeaters are excluded from model fitting.
optimx.args	Additional arguments to control the optimization which are forwarded to optimx::optimx. If multiple optimization methods are specified, only the result of the last method is further processed.
verbose	Show details about the running of the function.
...	Ignored

Details

Model parameters for the G/G model are p, q, and gamma.
p: shape parameter of the Gamma distribution of the spending process.
q: shape parameter of the Gamma distribution to account for customer heterogeneity.
gamma: scale parameter of the Gamma distribution to account for customer heterogeneity.
If no start parameters are given, p=0.5, q=15, gamma=2 is used for all model parameters. All parameters are required to be > 0.

The Gamma-Gamma model cannot be estimated for data that contains negative prices. Customers with a mean spending of zero or a transaction count of zero are ignored during model fitting.

The G/G model

The G/G model allows to predict a value for future customer transactions. Usually, the G/G model is used in combination with a probabilistic model predicting customer transaction such as the Pareto/NBD or the BG/NBD model.

Value

An object of class clv.gg is returned.

The function summary can be used to obtain and print a summary of the results. The generic accessor functions coefficients, vcov, fitted, logLik, AIC, BIC, and nobs are available.

References

Colombo R, Jiang W (1999). “A stochastic RFM model.” Journal of Interactive Marketing, 13(3), 2-12.

Fader PS, Hardie BG, Lee K (2005). “RFM and CLV: Using Iso-Value Curves for Customer Base Analysis.” Journal of Marketing Research, 42(4), 415-430.

Fader PS, Hardie BG (2013). “The Gamma-Gamma Model of Monetary Value.” URL http://www.brucehardie.com/notes/025/gamma_gamma.pdf.

See Also

clvdata to create a clv data object.

plot to plot diagnostics of the transaction data, incl. of spending.

predict to predict expected mean spending for every customer.

plot to plot the density of customer's mean transaction value compared to the model's prediction.

Examples

data("apparelTrans")
clv.data.apparel <- clvdata(apparelTrans, date.format = "ymd",
                            time.unit = "w", estimation.split = 52)

# Fit the gg model
gg(clv.data.apparel)

# Give initial guesses for the model parameters
gg(clv.data.apparel,
     start.params.model = c(p=0.5, q=15, gamma=2))


# pass additional parameters to the optimizer (optimx)
#    Use Nelder-Mead as optimization method and print
#    detailed information about the optimization process
apparel.gg <- gg(clv.data.apparel,
                     optimx.args = list(method="Nelder-Mead",
                                        control=list(trace=6)))

# estimated coefs
coef(apparel.gg)

# summary of the fitted model
summary(apparel.gg)

# Plot model vs empirical distribution
plot(apparel.gg)

# predict mean spending and compare against
#    actuals in the holdout period
predict(apparel.gg)

CLVTools documentation built on Oct. 13, 2024, 9:07 a.m.