52 / Journal of Marketing, September 2014

52 / Journal of Marketing, September 2014

Heerde 2011). Thus, the reported predictive performance of two customer types: a new customer without any repeat our model is conservative.

purchases (the majority of customers in our data) and an We calibrate all models using the first 104 weeks (i.e.,

established customer who made five repeat purchases, two years) and validate them using the remaining 26 weeks

which we assume split our observation period of 2.5 years (i.e., six months). Because there are no closed-form expres-

evenly so that each interpurchase time is 182 days. If there sions for expected future purchasing in the complaints and

is no complaint (the hassle-free case), the last event is a purchase-only models, we must simulate future purchases,

purchase, and we calculate RLV standing immediately after complaints, and churn following these two types of events.

the last purchase. If the last event is a complaint, we assume If there is a future complaint, we simulate whether the com-

it occurs 28 days—the empirical average time until a com- pany provides a recovery using the model estimates of

plaint is voiced—after the last purchase, and we calculate Equation 8. Each latent class has its own parameter esti-

RLV assuming that we stand immediately after this last com- mates (Table 1); we simulate from each class separately and

plaint. If the last event is a complaint, (1) it may be the only combine these simulations with the probabilities of class

complaint voiced (no prior complaints from this customer), membership to forecast the expected unconditional future

(2) there may have been a prior complaint voiced 28 days purchases. We use 1,000 simulations to forecast future pur-

before the current complaint (i.e., on the day of the most chasing. The standard error of the forecasts in the com- recent purchase), or (3) there may have been a prior com- plaints model is low, on average .007 purchases. plaint that occurred only 7 days before the current complaint. We judge model fit using two methods. Following the

customer base literature stream (e.g., Fader, Hardie, and

Procedure to Compute RLV

Lee 2005a, b; Van Oest and Knox 2011), we divide cus- tomers into groups according to how many repeat purchases

Fader, Hardie, and Lee (2005b) derive an expression for the they made in the calibration period (0, 1, ..., 6+) and com-

RLV of an already acquired customer, conditional on pute the average number of expected purchases in the vali-

observed behavior, by combining a model for the interpur- dation period in the Panel A of Figure B1. We also count the

chase time and churn processes with a separate model for number of customers best predicted by each model, as mea-

profit per transaction. We follow the same path by simulat- sured by the absolute error between the actual number of

ing future purchases, complaints, and churn following these purchases made by each customer in the validation period

two types of events until the inactive state is reached (i.e., and the model predictions, in Panel B of Figure B1.

for the entire residual lifetime of each customer). In the In Figure B1, Panel A, the grouped predictions figure

process, we keep track of (simulated) prior purchases and shows that the predictions of the complaints model (dashed

complaints. If there is a complaint, we simulate whether the line with squares) and the BG/NBD model (dashed line

company provides a recovery using the model estimates of with triangles) are substantially closer to the actual average

parameters d rec, 0 , d rec, 1 , and d rec, 2 in Table 1. 7 We impute number of purchases (the solid line) than the purchase-only

the company’s cost of providing recovery to a future com- model (dashed line with crosses). The absolute error is

plaint at $20. 8 We arrive at this cost estimate by considering lower for the complaints model than the purchase-only

a lost shipment: the average order size is $57.32, and the model in five of seven cases.

cost price of the shipped goods is 26% of this amount (i.e., The performance of the complaints model relative to the

approximately $15); we assume the reshipment itself costs BG/NBD model is more difficult to judge. The BG/NBD

approximately $5, resulting in $20 in total. Similar to model is closer to the actual (i.e., has a lower absolute

Schweidel and Knox (2013), we simulate separately for error) in four of seven cases, but the three cases in which

each latent class and combine these estimates with the the complaints model performs better account for more

probabilities of class membership. 9 We simulate purchase total customers than the BG/NBD model. For example, the

amount from a gamma-gamma distribution (Colombo and complaints model has a lower absolute error than the

Jiang 1999; Fader, Hardie, and Lee 2005b). The annual dis- BG/NBD model for the 9,897 customers who made zero

count rate is 10%.

repeat purchases in the calibration period, the largest group. Thus, we turn to Figure B1, Panel B, to observe, customer by customer, which model predicts best (in terms of having

7 Instead of using the recovery model in Equation 8 for future the lowest absolute error). Panel B shows that the com-

complaints, we also considered a policy of “always recover” or plaints model provides the best predictions for the majority

“never recover,” on the basis of the company’s response to the cur- rent complaint, which we manipulate in the various scenarios. The

of the customer base (56%). Therefore, we conclude that RLV results did not differ by more than 12%, and the substantive the complaints model characterizes future purchasing better

findings remained unaffected.

than the purchase-only model and the BG/NBD. 8 The RLV results change by less than 2% if the cost of recovery is reduced from $20 to $0; they do not critically depend on the

Appendix C: Simulation Procedure cost of recovery.

9 We weigh the classes by their posterior probabilities to incor-

for RLV

porate all information about unobserved class membership. Because prior purchases and complaints play a dual role (i.e., non-

The Scenarios Considered

stationarity in the customer’s churn probability and heterogeneity signaling), we also simulated RLV using prior probabilities (i.e.,

We always calculate RLV standing immediately after the class sizes). The RLV did not change by more than 10% in any last event, either a purchase or a complaint. We consider

scenario, and the substantive findings are robust.

Customer Complaints and Recovery Effectiveness / 53

FIGURE B1 Model Comparison Forecasts of Future Purchasing

A: Conditional Expectations of Purchasing

Actual 3 0 1 Complaints model Purchase-only model – 5 BG/NBD

Number of Repeat Purchases in Weeks 1–104 B: Percentage of Customers Most Accurately Predicted by Each Model

Complaints Model

Purchase-Only Model

BG/NBD

Percentage of Customers Best Predicted (with Minimum Absolute Error)

54 / Journal of Marketing, September 2014

Parameters and Fit of Gamma-Gamma Model for

close to the actual overall mean of $57.32. We visualize the

Purchase Amounts

fit of the gamma-gamma distribution by comparing it with The maximum likelihood estimates of the gamma-gamma

the actual distribution (using kernel smoothing) in Figure distribution (following the notation in Fader, Hardie, and

C1. Overall, the two distributions are very close. At $25, the Lee 2005b) are pˆ = 2.67, qˆ = 3.85, gˆ = 58.52. The model

actual mode is only slightly smaller than the gamma- prediction of the overall mean purchase amount is $54.82,

gamma mode ($26).

FIGURE C1 Gamma-Gamma Model Fit

.020 Actual (nonparametric density)

Gamma-gamma model

s ity .010

Average Transaction Value ($)

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