chapter 6: customer analytics part ii. 2 v. kumar and w. reinartz – customer relationship...
TRANSCRIPT
Chapter 6:
Customer Analytics Part II
2V. Kumar and W. Reinartz – Customer Relationship Management
Overview
Topics discussed:
Strategic customer-based value metrics
Popular customer selection strategies
Techniques to evaluate alternative customer selection strategies
3V. Kumar and W. Reinartz – Customer Relationship Management
Customer-based Value Metrics
Customer based Value
Metrics
Popular Strategic
RFMPast
Customer Value
LTV Metrics
SizeOf
Wallet
Transition Matrix
Share ofCategory
Reqt.
Share of Wallet
Customer Equity
4V. Kumar and W. Reinartz – Customer Relationship Management
Strategic Customer-based Value Metrics
RFM Value
Past Customer Value
Lifetime Value Metrics
Customer Equity
5V. Kumar and W. Reinartz – Customer Relationship Management
RFM Method
• Elapsed time since a customer last placed an order with the company
Recency
• Number of times a customer orders from the company in a certain defined period
Frequency
• Amount that a customer spends on an average transaction
Monetary value
RFM Value
Technique to evaluate customer behavior and customer value
Often used in practice
Tracks customer behavior over time in a state-space
6V. Kumar and W. Reinartz – Customer Relationship Management
RFM Method
Example
Customer base: 400,000 customers
Sample size: 40,000 customers
Firm’s marketing mailer campaign: $150 discount coupon
Response rate: 808 customers (2.02%)
7V. Kumar and W. Reinartz – Customer Relationship Management
RFM Method
Recency coding
Test group of 40,000 customers is sorted in descending order based on the criterion of
‘most recent purchase date’
The earliest purchasers are listed on the top and the oldest are listed at the bottom
The sorted data is divided into five equally sized groups (20% in each group)
The top-most group is assigned a recency code of 1, the next group
a code of 2 until the bottom-most group is assigned a code of 5
Analysis of customer response data shows that the mailer campaign got the highest
response from those customers grouped in recency code 1 followed by those in code 2
etc.
8V. Kumar and W. Reinartz – Customer Relationship Management
RFM Method: Response and Recency
Graph depicts the distribution of relative frequencies of customer groups assigned to recency codes 1 to 5
Highest response rate (4.5%) for the campaign was from customers in the test group who belonged to the highest recency quintile (recency code =1)
4.50%
2.80%
1.50%
1.05%
0.25%
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
1 2 3 4 5
Recency Code (1 - 5)
Cu
sto
mer
Res
po
nse
%
9V. Kumar and W. Reinartz – Customer Relationship Management
RFM Method: Response and Frequency
Graph depicts the response rate of each of the frequency-based sorted quintiles
The highest response rate (2.45%) for the campaign was from customers in the test group belonging to the highest frequency quintile (frequency code =1)
2.45% 2.22%
2.08%
1.67% 1.68%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
1 2 3 4 5
Frequency Code 1-5
Res
po
nse
Rat
e %
10V. Kumar and W. Reinartz – Customer Relationship Management
RFM Method: Response and Monetary Value
Customer data is sorted, grouped and coded with a value from 1-5
The highest response rate (2.35%) for the campaign was from those customers in the test group who belonged to the highest monetary value quintile (monetary value code =1)
2.35%
2.05% 1.95% 1.90% 1.85%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
1 2 3 4 5
Monetary Value Code (1-5)
Res
po
nse
Rat
e %
11V. Kumar and W. Reinartz – Customer Relationship Management
RFM Method: RFM procedure
Step 1
. . .
. . .
Last purchase: 1 day ago
Last purchase: 320 days ago
. . .
R=1
R=1
R=1
R=2
R=2
R=2
R=5
R=5
R=5
Group 1
Group 2
Step 2 Step 3
averageresponse rate
averageresponse rate
averageresponse rate
Group 3
12V. Kumar and W. Reinartz – Customer Relationship Management
RFM Method: Limitations
RFM method 1 independently links customer response data with R, F and M values and
then groups customers belonging to specific RFM codes
May not produce equal number of customers under each RFM cell since individual metrics
R, F, and M are likely to be somewhat correlated
For example, a person spending above average (high M) is also likely to spend more
frequently (high F)
For practical purposes, it is desirable to have exactly the same number of individuals in
each RFM cell
13V. Kumar and W. Reinartz – Customer Relationship Management
RFM Method: Cell Sorting Technique
A list of 40,000 test group of customers is first sorted for recency and then grouped into 5
groups of 8,000 customers each
The 8,000 customers in each group are sorted based on frequency and divided into five
equal groups of 1,600 customers each - at the end of this stage, there will be RF codes
starting from 11 to 55 with each group including 1,600 customers
In the last stage, each of the RF groups is further sorted based on monetary value and
divided into five equal groups of 320 customers each
RFM codes starting from 111 to 555 each including 320 customers
Considering each RFM code as a cell, there will be 125 cells (5 recency divisions * 5
frequency divisions * 5 monetary value divisions = 125 RFM Codes)
14V. Kumar and W. Reinartz – Customer Relationship Management
RFM Method: RFM Cell Sorting
1
2
3
4
5
41
42
43
44
45
41
42
43
44
45
Customer Database
R
F
11
12
13
14
15
11
12
13
14
15
M
Sorted Once Sorted Five Times per R Quintile
Sorted Twenty-Five Times per R Quintile
131
132
133
134
135
441
442
443
444
445
1
2
3
4
5
131
132
133
134
135
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RFM Method: Breakeven Value (BE)
Breakeven = net profit from a marketing promotion equals the cost associated with
conducting the promotion
Breakeven Value (BE) = unit cost price / unit net profit
BE computes the minimum response rates required in order to offset the promotional costs
involved and thereby not incur any losses
Example
Mailing $150 discount coupons
The cost per mailing piece is $1.00
The net profit (after all costs) per used coupon is $45,
Breakeven Value (BE) = $1.00/$45 = 0.0222 or 2.22%
16V. Kumar and W. Reinartz – Customer Relationship Management
RFM Method: Breakeven Index
Breakeven Index (BEI) = ((Actual response rate – BE) / BE)*100
Example
If the actual response rate of a particular RFM cell was 3.5%
BE is 2.22%,
The BEI = ((3.5% - 2.22%)/2.22%) * 100 = 57.66
Positive BEI value some profit was made from the group of customers
0 BEI value the transactions just broke even
Negative BEI value the transactions resulted in a loss
17V. Kumar and W. Reinartz – Customer Relationship Management
RFM Method: Combining RFM codes, breakeven codes, breakeven index
Cell # RFM codes Cost per mail $ Net profit per sale ($)
Breakeven (%) Actual response (%)
Breakeven index
1 111 1 45.00 2.22 17.55 6902 112 1 45.00 2.22 17.45 6853 113 1 45.00 2.22 17.35 6814 114 1 45.00 2.22 17.25 6765 115 1 45.00 2.22 17.15 6726 121 1 45.00 2.22 17.05 6677 122 1 45.00 2.22 16.95 6638 123 1 45.00 2.22 16.85 6589 124 1 45.00 2.22 16.75 65410 125 1 45.00 2.22 16.65 64911 131 1 45.00 2.22 16.55 64512 132 1 45.00 2.22 16.45 64013 133 1 45.00 2.22 16.35 63614 134 1 45.00 2.22 16.25 63115 135 1 45.00 2.22 16.15 62716 141 1 45.00 2.22 16.05 62217 142 1 45.00 2.22 15.95 61818 143 1 45.00 2.22 15.85 61319 144 1 45.00 2.22 15.75 60920 145 1 45.00 2.22 15.65 60421 151 1 45.00 2.22 15.55 60022 152 1 45.00 2.22 15.45 59523 153 1 45.00 2.22 15.35 59124 154 1 45.00 2.22 15.25 58625 155 1 45.00 2.22 15.15 58226 211 1 45.00 2.22 15.65 60427 212 1 45.00 2.22 15.55 60028 213 1 45.00 2.22 15.45 59529 214 1 45.00 2.22 15.35 59130 215 1 45.00 2.22 15.25 58631 221 1 45.00 2.22 15.15 58232 222 1 45.00 2.22 15.05 57733 223 1 45.00 2.22 14.95 57334 224 1 45.00 2.22 14.85 56835 225 1 45.00 2.22 14.75 564
18V. Kumar and W. Reinartz – Customer Relationship Management
RFM codes versus BEI
0
200
400
600
800
1000
1200
1400
111
132
153
224
245
321
342
413
434
455
531
552
RFM Cell Codes
BE
I Break-Even Index
19V. Kumar and W. Reinartz – Customer Relationship Management
RFM and BEI
Customers with higher RFM values tend to have higher BEI values
Customers with a lower recency value but relatively highF and M values tend to have
positive BEI values
Customer response rate drops more rapidly for the recency metric
Customer response rate for the frequency metric drops more rapidly than the one for the
monetary value metric
20V. Kumar and W. Reinartz – Customer Relationship Management
Comparison of profits for targeting campaign test
Test Full customer base RFM Selection
Average response rate 2.02% 2.02% 15.25%
# of responses 808 8,080 2,732.8
Average Net profit/Sale $45 $45 $45
Net Revenue $36,360 $363,600 $122,976
# of Mailers sent 40,000 400,000 17,920
Cost per mailer $1.00 $1.00 $1.00
Mailing cost $40,000.00 $400,000.00 $17,920.00
Profits (-$3,640.00) ($36,400.00) $105,056.00
21V. Kumar and W. Reinartz – Customer Relationship Management
Relative Importance of R, F, and M
Regression techniques to compute the relative weights of the R, F, and M metrics
Relative weights are used to compute the cumulative points of each customer
The pre-computed weights for R, F and M, based on a test sample are used to assign RFM
scores to each customer
The higher the computed score, the more likely the customer will be profitable in future
This method is flexible and can be tailored to each business situation
22V. Kumar and W. Reinartz – Customer Relationship Management
Recency Score
20 if within past 2 months, 10 if within past 4 months, 05 if within past 6 months, 03 if within
past 9 months, 01 if within past 12 months, relative weight = 5
Customer Purchase
Number
Recency
(Month)
Assigned
Points
Weighted
Points
1 2 20 100
John 2 4 10 50
3 9 3 15
Smith 1 6 5 25
1 2 20 100
Mags 2 4 10 50
3 6 5 25
4 9 3 15
23V. Kumar and W. Reinartz – Customer Relationship Management
Frequency Score
Points for Frequency: 3 points for each purchase within 12 months; Maximum = 15 points;
Relative weight = 2
Customer Purchase Number
Frequency Assigned Points
Weighted Points
1 1 3 6
John 2 1 3 6
3 1 3 6
Smith 1 2 6 12
1 1 3 6
Mags 2 1 3 6
3 2 6 12
4 1 3 6
24V. Kumar and W. Reinartz – Customer Relationship Management
Monetary Value Score
Monetary Value: 10 percent of the $-value of purchase with 12 months; Maximum = 25
points; Relative weight = 3
Customer Purchase Number
Value of purchase ($)
Assigned Points
Weighted Points
1 $40 4 12
John 2 $120 12 36
3 $60 6 18
Smith 1 $400 25 75
1 $90 9 27
Mags 2 $70 7 21
3 $80 8 24
4 $40 4 12
25V. Kumar and W. Reinartz – Customer Relationship Management
Cumulative scores: 249 for John, 112 for Smith and 308 for Mags, indicates a potential
preference for Mags John seems to be a good prospect, but mailing to Smith might be a misdirected marketing
effort
Customer Purchase Number
Total Weighted Points
Cumulative Points
1 118 118 John 2 92 210
3 39 249
Smith 1 112 112
1 133 133
Mags 2 77 210
3 61 271
4 37 308
26V. Kumar and W. Reinartz – Customer Relationship Management
Past Customer Value
Computation of Customer Profitability (PCV)
PCV of customer i
Where: i = number representing the customer,
t = time index,
= applicable discount rate (for example 1.25% per month),
t0 = current time period,
T = number of time periods prior to current period that should be
considered, GCin = gross contribution of transaction of customer in period t
Since products / services are bought at different points in time during the customer’s lifetime,
all transactions have to be adjusted for the time value of money
Limitations
Equation does not consider whether a customer is going to be active in the future and it
does not incorporate the expected cost of maintaining the customer in the future
T
t
tnttiGC
0
)1(*0
27V. Kumar and W. Reinartz – Customer Relationship Management
Spending Pattern of a Customer
PCVi = 6*(1+0.0125)o +9*(1+0.0125)1 +15*(1+0.0125)2 +15*(1+0.0125)3+ 240*(1+0.0125)4
= 302.01486
The customer is worth $302.01 expressed in net present value in May dollars
Comparing the PCV of a set of customers leads to a prioritization of directing future
marketing efforts
Jan Feb March April May
Purchase Amount ($) 800 50 50 30 20
GC 240 15 15 9 6
Gross contribution (GC) = purchase amount X contribution margin
28V. Kumar and W. Reinartz – Customer Relationship Management
Lifetime Value Metrics
Multi-period evaluation of a customer’s value to the firm
Lifetime Value (LTV)
Recurring
Revenues
Recurring costs
Contribution margin
Lifetime of a customer
Lifetime Profit
Acquisition cost
LTVDiscount rate
Lifetime of a customer
Discount rate
29V. Kumar and W. Reinartz – Customer Relationship Management
Basic LTV Model
Where: i = customer,
t = time period,
= interest (or discount) rate,
= gross contribution of customer i at time t,
T = observation time horizon,
= lifetime value of an individual customer i at net present value time
t=0
30V. Kumar and W. Reinartz – Customer Relationship Management
Basic LTV Model
LTV is a measure of a single customer’s worth to the firm
Used for pedagogical and conceptual purposes
Information source
CM and T from managerial judgment or from actual purchase data.
The interest rate, a function of a firm’s cost of capital, can be obtained from financial
accounting
Evaluation
Typically based on past customer behavior and may have limited diagnostic value for
future decision-making Caution: If the time unit is different from a yearly basis, the interest rate needs to be adjusted accordingly. !
31V. Kumar and W. Reinartz – Customer Relationship Management
LTV with Splitted Revenues and Costs
Where: i = customer,
t = time period,
= interest (or discount) rate,
T = observation time horizon,
= sales value to customer i at time t,
= direct costs of products by customer i at time t,
= marketing costs directed at customer i at time t,
= lifetime value of an individual customer i at net present value
time t=0
32V. Kumar and W. Reinartz – Customer Relationship Management
LTV with Splitted Revenues and Costs
The cost element of this example is broken down into direct product-related costs and
marketing costs
Depending on data availability, it can be enhanced by including service-related cost,
delivery cost, or other relevant cost elements
33V. Kumar and W. Reinartz – Customer Relationship Management
LTV Including Customer Retention Probabilities
Where: i = customer,
t = time period,
= interest (or discount) rate,
T = observation time horizon,
= average retention rate at time t (it is possible to use an individual
level retention probability but usually this is difficult to obtain),
= gross contribution of customer i at time t,
= costs of acquiring customer i (acquisition costs)
34V. Kumar and W. Reinartz – Customer Relationship Management
LTV Including Customer Retention Probabilities
In this equation the term is actually the survival rate
The retention rate is constant over time and thus the expression can be simplified using the
identity:
35V. Kumar and W. Reinartz – Customer Relationship Management
LTV with Constant Retention Rate and Gross Contribution
Assuming that T and that the retention rate and the contribution margin (CM) do not vary
over time:
The margin multiplier:
How long is the Lifetime Duration?
For all practical purposes, the lifetime duration is a longer-term duration used
managerially
It is important to make an educated judgment regarding a sensible duration horizon in
the context of making decisions
36V. Kumar and W. Reinartz – Customer Relationship Management
LTV with Constant Retention Rate and Gross Contribution
Incorporating externalities in the LTV
The value a customer provides to a firm does not only consist of the revenue stream
that results from purchases of goods and services
Product rating websites, weblogs and the passing on of personal opinions about a
product or brand co-contribute substantially to the lifetime value of a customer
These activities are subsumed under the term word-of mouth (WOM)
37V. Kumar and W. Reinartz – Customer Relationship Management
Measuring and Incorporating Word-of-Mouth (WOM)
Where: i = customer,
t = time period,
= interest (or discount) rate,
T = observation time horizon,
= average retention rate at time t,
= gross contribution of customer i at time t,
= number of new acquisition at time t due to referrals customer i,
= average acquisition cost savings per customer gained through
referral of customer i at time t,
= costs of acquiring customer i (acquisition costs)
38V. Kumar and W. Reinartz – Customer Relationship Management
This table is adapted from Kumar, Petersen , and Leone (2007)
Customer Value Matrix
Average CRV after 1 year
Low High
Average LTV after 1 year
High Affluents Champions
Low Misers Advocates
39V. Kumar and W. Reinartz – Customer Relationship Management
LTV
Alternative ways to account for externalities
The value of a customer’s referrals can be separated from the LTV, for example by
calculating a separate customer referral value (CRV) for each customer
A joined evaluation of both metrics helps the management to select and determine
how to develop its customers
Information source
Information on sales, direct cost, and marketing cost come from internal company
records
Many firms install activity-based-costing (ABC) schemes to arrive at appropriate
allocations of customer and process-specific costs
Evaluation
LTV (or CLV) is a forward looking metric that is appropriate for long-term decision
making
It is a flexible measure that has to be adapted to the specific business context of an
industry
40V. Kumar and W. Reinartz – Customer Relationship Management
Customer Equity
Customer equity (CE) = Sum of the LTV of all the customers of a firm
Where: i = customer,
I = all customers of a firm (or specified customer cohort or segment),
LTVi = lifetime value of customer i
Indicator of how much the firm is worth at a particular point in time as a result of the firm’s
customer management efforts
Can be seen as a link to the shareholder value of a firm
41V. Kumar and W. Reinartz – Customer Relationship Management
Customer Equity
Customer Equity Share (CES):
Where: CEj = customer equity of brand j,
j = focal brand,
K = all brands a firm offers
Information source
Basically the same information as for the LTV is required
Evaluation
The CE represents the value of the customer base to a company
The metric can be seen as an indicator for the shareholder value of a firm
42V. Kumar and W. Reinartz – Customer Relationship Management
Customer Equity Calculation Example
15,006Total customer
equity
1,1799161310.1310.8520360.31204
1,68311161530.1530.8220360.31203
2,24412161870.1870.7520360.31202
3,50014162500.250.6320360.31201
6,40016164000.40.420360.31200
11. TotalDisctd.Profits perPeriod to theManufactu-rer
10. Discount
edProfit perCustome
r per Period to Manufact
u-rer
9Profit perCustomer per period per Manu-facturer
8. Expecte
dNumber
ofActive
Customer
7. Surviv
alRate
6.ActualRetention Rate
5. Mktg and
Servicing
Costs
4. Manufac-turerGross Margin
3.Manuf
a-cturerMargin
2Sales perCustomer
1Year fromAcquis-ition
43V. Kumar and W. Reinartz – Customer Relationship Management
Popular Customer Selection Strategies
Techniques
Profiling
Binary Classification Trees
Logistic regression
Techniques to Evaluate Customer Selection Strategies
Missclassification Rate
Lift Analysis
CRM at Work: Tesco
Example where a company combines analytical skills, judicious judgment, knowledge
about consumer behavior and careful targeting of customers
44V. Kumar and W. Reinartz – Customer Relationship Management
Profiling
The intuitive approach for customer selection is based on the assumption that the most
profitable customers share common characteristics
Based on this assumption the company should try to target customers with similar profiles
to the currently most profitable ones
Disadvantage
Only customers that are similar to existing ones are considered
Profitable customer segments that do not match the current customer base might be
missed
45V. Kumar and W. Reinartz – Customer Relationship Management
Profiling: Using Profiling for New Customer Acquisition
Transactions, demographics, lifestyle Demographics, lifestyle
Current
Customers
B C
Potential
Customers
E D
A
F
Individual A
Individual B
Individual C
Individual 1
Individual 2
Individual 3
Response Variable
Internal Variables
ExternalVariables
46V. Kumar and W. Reinartz – Customer Relationship Management
Binary Classification Trees
Used to identify the best predictors of a 0/1 or binary dependent variable
Useful when there is a large set of potential predictors for a model
Classification tree algorithms can be used to iteratively search the data to find out which
predictor best separates the two categories of a binary (or more generally categorical)
target variable
47V. Kumar and W. Reinartz – Customer Relationship Management
Binary Classification Trees
The algorithm procedure
1. To find out which of the explanatory variables Xi best explains the outcome Y, calculate
the number of misclassifications
2. Use the variable Xi with the lowest misclassification rate to separate the customer base
3. This process can be repeated for each sub segment until the misclassification rate
drops below a tolerable threshold or all of the predictors have been applied to the
model
Evaluation Problem with the approach: prone to over-fitting The model developed may not perform nearly as well on a new or separate dataset
48V. Kumar and W. Reinartz – Customer Relationship Management
Binary Classification Trees: Classification of Potential Hockey Equipment Buyers
Male
Bought hockey
Did not buy hockey
Female
Bought hockey
Did not buy hockey
Total
Bought hockey
Did not buy hockey
Bought scuba
60 1,140 50 1,550 110 2,690
Did not buy scuba
1,540 2,860 80 1,320 1,620 4,180
Total 1,600 4,000 130 2,870 1,730 6,870
49V. Kumar and W. Reinartz – Customer Relationship Management
Binary Classification Trees: Classification of Potential Hockey Equipment Buyers
Possible separations of potential hockey equipment buyers
Step 1
Separation by gender
1,600 bought hockey equipment
Male: 5,600
4,000 did not buy hockey equipment
130 bought hockey equipment
Female: 3,000
2,870 did not buy hockey equipment
Separation by purchase of scuba
equipment 110 bought hockey equipment
Bought: 2,800
2,690 did not buy hockey equipment
1,620 bought hockey equipment
Did not buy: 5,800
4,180 did not buy hockey equipment
50V. Kumar and W. Reinartz – Customer Relationship Management
Binary Classification Trees: Classification of Potential Hockey Equipment Buyers
Classification of hockey buyers by gender
Step 2
Buyer
Yes 1730No 6870
Total 8600
Male
Buyer
Yes 1,600
No
4,000
Total
5,600
Female
Buyer
Yes
130
No
2,870
Total
3,000
Gender
51V. Kumar and W. Reinartz – Customer Relationship Management
Binary Classification Trees: Classification of Potential Hockey Equipment Buyers
Classification tree for hockey equipment buyers Step 3
Male Buyer Yes 1,600 No 4,000Total 5,600
Bought scubaBuyer Yes 60No 1,140
Total 1,200
Not bought scubaBuyer Yes 1,540No 2,860
Total 4,400
Female Buyer Yes 130 No 2,870Total 3,000
MarriedBuyer Yes 100No 2,000
Total 2,100
Not marriedBuyer Yes 30No 870
Total 900
Buyer Yes 1730No 6870
Total 8600
Gender
Bought scuba equipment Marital status
52V. Kumar and W. Reinartz – Customer Relationship Management
Logistic Regression
Method of choice when the dependent variable is binary and assumes only two discrete
values
By inputting values for the predictor variables for each new customer – the logistic model
will yield a predicted probability
Customers with high ‘predicted probabilities’ may be chosen to receive an offer since they
seem more likely to respond positively
53V. Kumar and W. Reinartz – Customer Relationship Management
Logistic Regression: Examples
Example 1: Home ownership
Home ownership as a function of income can be modeled whereby ownership is
delineated by a 1 and non-ownership a 0
The predicted value based on the model is interpreted as the probability that the
individual is a homeowner
With a positive correlation between increasing income and increasing probability of
ownership, one can expect results as
Predicted probability of ownership is .22 for a person with an income of $35,000
Predicted probability of .95 for a person with a $250,000 income
54V. Kumar and W. Reinartz – Customer Relationship Management
Logistic Regression: Examples
Example 2: Credit Card Offering
Dependent Variable - whether the customer signed up for a gold card offer
Predictor Variables - other bank services the customer used plus financial and
demographic customer information
By inputting values for the predictor variables for each new customer, the logistic model
will yield a predicted probability
Customers with high ‘predicted probabilities’ may be chosen to receive the offer since
they seem more likely to respond positively
55V. Kumar and W. Reinartz – Customer Relationship Management
Linear and Logistic Regression
In linear regression, the effect of one unit change in the independent variable on the
dependent variable is assumed to be a constant represented by the slope of a straight line
For logistic regression the effect of a one-unit increase in the predictor variable varies along
an s-shaped curve . At the extremes, a one-unit change has very little effect, but in the
middle a one unit change has a fairly large effect
56V. Kumar and W. Reinartz – Customer Relationship Management
Logistic Regression: Formula
Where: y= dependent variable,
x= predictor variable,
= constant (which is estimated by linear regression and often
called intercerpt),
= the effect of x on y (also estimated by linear regression),
= error term
57V. Kumar and W. Reinartz – Customer Relationship Management
Logistic Regression: Transformation Steps
Step 1: If p represents the probability of an event occurring, take the ratio
Since p is a positive quantity less than 1, the range of this expression is 0 to infinity
Step 2: Take the logarithm of this ratio:
This transformation allows the range of values for this expression to lie between
negative infinity and positive infinity
p
p
1
pp
1log
58V. Kumar and W. Reinartz – Customer Relationship Management
Logistic Regression: Transformation Steps
Step 3: The value can be considered as the dependent variable and a linear
relationship of this value with predictor variables in the form z = can be written.
and coefficients can be estimated
Step 4: In order to obtain the predicted probability p, a back transformation is to be done:
Since = z =
Then calculate the probability p of an event occurring, the variable of interest, as
pp
1log
59V. Kumar and W. Reinartz – Customer Relationship Management
Logistic Regression: Interpretation of Coefficients
Interpret the coefficients carefully
If the logit regression coefficient β = 2.303
When the independent variable x increases one unit, the odds that the dependent
variable equals 1 increase by a factor of 10, keeping all other variables constant.
Sample of contract extension and sales Contract extension Number of sales calls
1 21 40 60 21 41 80 30 00 20 50 01 21 81 4
60V. Kumar and W. Reinartz – Customer Relationship Management
Logistic Regression: Interpretation of Coefficients Odds of Logistic Regression Example
It expects that sales calls impact the probability of contract extension. Thus, it estimates the
model:
Prob (contract extension)
The resulting estimates are: α= -1.37; β= 0.39
Odds of logistic regression example
Sales calls = 0 Sales calls = 1
Odds (exp(α+β *sales calls))
0.253 0.375
Probability of contract extension
0.202 0.273
Difference in probabilities 0.071
)(1
1callssales
e
61V. Kumar and W. Reinartz – Customer Relationship Management
Logistic Regression: Evaluation
Evaluation
For logistic regression the effect of a one-unit increase in the predicor variable varies
along an s-shaped curve
This means that at the extremes, a one-unit change has a very little effect, but in the
center a one-unit change has a fairly large effect
62V. Kumar and W. Reinartz – Customer Relationship Management
Techniques to Evaluate Alternative Customer Selection Strategies
A critical step to decide which model to use for selecting and targeting potential customers
is to evaluate alternative selection strategies
When several alternative models are available for customer selection, we need to compare
their relative predition quality
Divide the data into a training (calibration) dataset (2/3 of the data) and a holdout (test)
sample (1/3 of the data)
The models are estimated based on the training dataset
Select the model that generalizes best from the training to the data
Techniques
Misclassification Rate
Lift Analysis
63V. Kumar and W. Reinartz – Customer Relationship Management
Misclassification Rate
Estimate the different models on two thirds of the available data
Calculate the misclassificaion rate on the remaining third to check for model performance
Example
The number of mispredictions is the sum of the off-diagonal entries (56+173=229)
Misclassification Rate: 229/ 1,459 = 15,7%
Predicted1 0 Totals
Observed 1 726 56 782
0 173 504 677
Totals 899 560 1,459
64V. Kumar and W. Reinartz – Customer Relationship Management
LIFT Analysis
Lift Charts
Lifts charts show how much better the current model performs against the results
expected if no model was used (base model)
Can be used to track a model’s performance over time, or to compare a model’s
performance on different samples
Lift% = (Response rate for each decile) / (Overall response rate) *100
Cumulative lift% = (Cumulative response rate) / (Overall response rate) *100
Cumulative response rate = cumulative number of buyers / Number of customers per
decile
65V. Kumar and W. Reinartz – Customer Relationship Management
Lift Performance Illustration
Lift and Cumulative Lift
Number of decile
Number of customers
Number of buyers
Response rate %
Lift Cumulative lift
1 5,000 1,759 35.18 3.09 3.09
2 5,000 1,126 22.52 1.98 5.07
3 5,000 998 19.96 1.75 6.82
4 5,000 554 11.08 0.97 7.80
5 5,000 449 8.98 0.79 8.59
6 5,000 337 6.74 0.59 9.18
7 5,000 221 4.42 0.39 9.57
8 5,000 113 2.26 0.20 9.76
9 5,000 89 1.78 0.16 9.92
10 5,000 45 0.90 0.08 10.00
Total 50,000 5,691 11.38
66V. Kumar and W. Reinartz – Customer Relationship Management
Lift Performance Illustration
The Decile analysis distributes customers into ten equal size groups
For a model that performs well, customers in the first decile exhibit the highest response
rate
Decile Analysis
35.18%
22.52%19.96%
11.08%8.98%
6.74%4.42%
2.26% 1.78% 0.90%
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
40.00%
1 2 3 4 5 6 7 8 9 10
Deciles
Re
sp
on
se
Ra
te
67V. Kumar and W. Reinartz – Customer Relationship Management
Lift Performance Illustration
Lifts that exceed 1 indicate better than average performance
Less than 1 indicate a poorer than average performance
For the top decile the lift is 3.09; indicates that by targeting only these customers are
expected to yield 3.09 times the number of buyers found by randomly mailing the same
number of customers
Lift Analysis
3.09
1.981.75
0.970.79
0.590.39
0.20 0.16 0.08
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
1 2 3 4 5 6 7 8 9 10
Deciles
Lift
68V. Kumar and W. Reinartz – Customer Relationship Management
Lift Performance Illustration
The cumulative lifts for the model reveal what proportion of responders we can expect to
gain from targeting a specific percentage of customers using the model
Choosing the top 30 % of the customers from the top three deciles will obtain 68% of
the total responders
Cumulative Lift Analysis
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Decile
Cu
mu
lati
ve
Lif
t
69V. Kumar and W. Reinartz – Customer Relationship Management
Lift Performance Illustration
Logistic models tend to provide the best lift performance
The past customer value approach provides the next best performance
The traditional RFM approach exhibits the poorest performance
Comparison of Models
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Deciles
Cu
mu
lati
ve L
ift
Logistic
Past Customer Value
RFM
No Model
70V. Kumar and W. Reinartz – Customer Relationship Management
Minicase: Akzo Nobel, NV- Differentiating Customer Service According to Customer Value
One of the world's largest chemical manufacturers and paint makers
The polymer division, which serves exclusively the B-to-B market, established a “tiered
customer service policy” in the early 2000’s
Company developed a thorough list of all possible service activities that is currently offered
To formalize customer service activities, the company implemented a customer scorecard
mechanism to measure and document contribution margins per individual customer
Service allocation, differentiated as:
Services are free for all types of customers
Services are subject to negotiation for lower level customer groups
Services are subject to fees for lower level customers
Services are not available for the least valuable set of customers
71V. Kumar and W. Reinartz – Customer Relationship Management
Summary
The higher the computed RFM score, the more profitable the customer is expected to be in
the future
The PCV is another important metric, in which the value of a customer is determined
based on the total contribution (toward profits) provided by the customer in the past after
adjusting for the time value of money
The LTV reflects the long-term economic value of a customer
The sum of the LTV of all the customers of a firm represents the customer equity (CE)
Firms employ different customer selection strategies to target the right customers
Lift analysis, decile analysis and cumulative lift analysis are various techniques firms use to
evaluate alternative selection strategies
Logistic Regression is superior to past customer value and RFM techniques