More on RFM and Logistic: Lifts and Gains

Transcription

1 More on RFM and Logistic: Lifts and Gains

2 How do we conduct RFM in practice? Sample size Rule of thumb for size: Average number of responses per cell >4 4/ response rate = number to mail per cell e.g. response rate 2% --> 4/0.02=200 (times 125 RFM cells) Number of N-tiles With relatively small customer databases - quintiles may be too many For very large databases cells may be too few Don t have to be equal could have 5 (R), 3 (F), 4 (M) categories RFM isn t restricted to R, F, and M For websites could be R, F, and D (duration of visit)

3 What marketing program would you propose for these cells? R F M best, 5-worst

4 Lessons about RFM RFM analysis is Effective Simple Intuitive Flexible Does not require sophisticated software or analytics Anyone can do it RFM can handle only few predictive variables There may be much more predictive information (logistic is solution)

5 How do we assess model s performance and compare it to that of different models? Model performance measures General approach We are generally interested in models that predict or classify Use model to rank/score customers Calculate improvement in response over no targeting Lifts Expected number of customers relative to random targeting Gains Percentage of total buyers we expect from targeting X% of customers

6 We are using RFM for Tuscan Lifestyles to estimate lifts Approach for calculation of lifts Perform RFM Organize cells in deciles by response rate (variable buyer) Estimate lifts by comparing response rates in deciles and base response rate Dataset tuscan_lg Contains independent and sequential RFM indices

7 Lifts in RFM Prediction model /*split in 10 groups by mean response rate for independent N-tile RFM*/ proc rank data=tuscan_lg out=tuscan_lift1 ties=low groups=10; var resp1; We use average response rate ranks lift_iq; to form deciles run; We are reversing order of data tuscan_lift; deciles so best customers are set tuscan_lift1; in decile 1 lift_iq=10-lift_iq; run; proc freq data=tuscan_lift ; tables lift_iq*buyer /norow nocum nopercent ; run;

8 Lifts in RFM Prediction model We formed deciles by response rate

9 Calculation of Lift: Independent N-tile RFM Score Decile # Customers Cum # Cum % # Buyers Cum # Response Lift Cum. Resp. Cum. Lift Customers Customers Buyers Rate Rate % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 1.00 Total % Cumulative # customers: the number of total customers up to and including that decile Cumulative % customers: the percent of total customers up to and including that decile Cumulative # Buyers: the number of buyers up to and including that decile Response Rate: the actual response rate for each decile, computed by the number of buyers divided by the number of customers for each decile Lift: (response rate for each decile) / (overall response rate) Cumulative Response Rate: cumulative # buyers / cumulative # customers Cum(ulative) Lift: (cumulative response rate) / (overall response rate) *100

10 The Lift indicates the model s ability to beat the no model Lift for top decile is 2.33 Targeting only top decile will yield 2.33 more responses/buyers than if we had not targeted Lift is relative index, i.e lift is 2.33 times base rate (2.46%)

11 Calculation of Gains: Independent N-Tile RFM Score Decile # Customers Cum # Cum % # Buyers Cum # Gains Cum. Gains Customers Customers Buyers % % 22.06% % % 38.25% % % 50.78% % % 61.11% % % 70.43% % % 78.32% % % 85.15% % % 90.26% % % 95.44% % % % Total % Gains the proportion of buyers in each decile Cum(ulative) Gains - the proportion of responders/buyers up to and including the decile, or simply the sum of the gains up to that decile.

12 Gains Chart The Gains chart reveals what proportion of responders we can expect to gain from targeting a specific percent of customers using the model By using the RFM model to target only top decile we can get 22.06% buyers We can get 50.78% customers by targeting three top deciles

13 Lifts and gains for sequential RFM /*split in 10 groups by mean response rate for sequential N-tile RFM*/ proc rank data=tuscan_lg out=tuscan_lift1 ties=low groups=10; var resp2; We use average response rate ranks lift_sq; to form deciles run; We are reversing order of data tuscan_lift; deciles so best customers are set tuscan_lift1; in decile 1 lift_sq=10-lift_sq; run; proc freq data=tuscan_lift ; tables lift_sq*buyer /norow nocum nopercent ; run;

14 Lifts and Gains in Sequential RFM

15 Calculation of Lift: Sequential N-tile RFM Score Decile # Customers Cum # Cum % # Buyers Cum # Response Lift Cum. Resp. Cum. Lift Customers Customers Buyers Rate Rate % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 1.00 Total % Cumulative # customers: the number of total customers up to and including that decile Cumulative % customers: the percent of total customers up to and including that decile Cumulative # Buyers: the number of buyers up to and including that decile Response Rate: the actual response rate for each decile, computed by the number of buyers divided by the number of customers for each decile Lift: (response rate for each decile) / (overall response rate) Cumulative Response Rate: cumulative # buyers / cumulative # customers Cum(ulative) Lift: (cumulative response rate) / (overall response rate) *100

16 Lift chart for sequential RFM Lift for top decile is 2.41

17 Calculation of Gains: Sequential N-Tile RFM Score Decile # Customers Cum # Cum % # Buyers Cum # Gains Cum. Gains Customers Customers Buyers % % 22.86% % % 39.48% % % 50.95% % % 61.83% % % 70.48% % % 78.07% % % 84.94% % % 90.81% % % 96.12% % % % Total % Gains the proportion of buyers in each decile Cum(ulative) Gains - the proportion of responders/buyers up to and including the decile, or simply the sum of the gains up to that decile.

18 Gains chart for sequential RFM Top decile contains 22.86% customers By using three top deciles we can get 50.96% customers

19 Logistic Regression proc logistic data=tuscan_lg descending plots=none; model buyer=last totdol numords; output out=tuscan_pr p=resp_pr; run; Let s see whether logistic regression provides better results.

20 Logistic Regression proc rank data=tuscan_pr out=tuscan_lift1 ties=low groups=10; var resp_pr; ranks lift_log; run; data tuscan_lift; set tuscan_lift1; lift_log=10-lift_log; run; proc freq data=tuscan_lift ; We use average response rate to form deciles We are reversing order of deciles so best customers are in decile 1 tables lift_log*buyer /norow nocum nopercent ; run;

21 Output for Logistic Regression

22 Lifts and Gains for Logistic Regression

23 Calculation of Lift: Logistic Regression Score Decile # Customers Cum # Cum % # Buyers Cum # Response Lift Cum. Resp. Cum. Lift Customers Customers Buyers Rate Rate % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 1.00 Total % Cumulative # customers: the number of total customers up to and including that decile Cumulative % customers: the percent of total customers up to and including that decile Cumulative # Buyers: the number of buyers up to and including that decile Response Rate: the actual response rate for each decile, computed by the number of buyers divided by the number of customers for each decile Lift: (response rate for each decile) / (overall response rate) Cumulative Response Rate: cumulative # buyers / cumulative # customers Cum(ulative) Lift: (cumulative response rate) / (overall response rate) *100

24 Calculation of Gains: Logistic Regression Score Decile # Customers Cum # Cum % # Buyers Cum # Gains Cum. Gains Customers Customers Buyers % % 22.52% % % 36.10% % % 47.74% % % 57.70% % % 66.85% % % 73.94% % % 80.68% % % 88.40% % % 94.56% % % % Total % Gains the proportion of buyers in each decile Cum(ulative) Gains - the proportion of responders/buyers up to and including the decile, or simply the sum of the gains up to that decile.

25 Lift chart for Logistic regression Lift for top decile is 2.25

26 Gains chart for Logistic regression Targeting top decile gets 22.86% customers

27 Lifts and Gains can be used to compare different models

28 Lifts and Gains can be used to compare different models The fatter then banana the better model!

29 Concordance vs. Lifts for Logistic Regression Concordance proportion of observations that may be correctly predicted (buyer=0 or buyer=1) by logistic regression 59.4% cases may be correctly classified The highest lift is 2.25, which corresponds to 5.53% response rate for top decile. Interpretation?