Predicting customer lifetime value

By Alex Labuda

November 27, 2022

Customer Lifetime Value

CLV with Machine Learning using RFM Features

In this blog we will wrangle customer spend and behavior data to engineer recency, frequency and monetary value features as input to our model which will predict the probability of a customer spending, as well as how much they are predicted to spend.

This can help marketers identify and target customers they are highly likely to spend, as well customers that are highly likely to spend even more.

library(tidymodels)
library(vip)
library(tidyverse)
library(timetk)
library(lubridate)
library(gt)

Data Prep

date customer_id order_total product_name1 product_name2 product_name3 product_name4 product_name5 product_category1 product_category2 product_category3 product_category4 product_category5
1/26/2022 N241027 42.00 CPR/AED Smart Certification App NA NA NA NA Continuing Education NA NA NA NA
1/26/2022 N1290714 495.73 Personal Trainer Basic Study Program CPR/AED Smart Certification App NA NA NA Publications Continuing Education NA NA NA
1/26/2022 N1290986 491.00 Group Fitness Instructor Advantage Program CPR/AED Smart Certification App NA NA NA Publications Continuing Education NA NA NA
1/26/2022 N1290942 119.96 The Professional’s Guide to Health and Wellness Coaching - eBook only NA NA NA NA Publications NA NA NA NA
1/26/2022 N885586 524.37 Personal Trainer Plus Study Program NA NA NA NA Publications NA NA NA NA 
cdnow_tbl <- cust_raw %>%
    select(date, customer_id, order_total) %>%
    set_names(
        c("date", "customer_id", "price")
    ) %>%
    mutate(date = mdy(as.character(date))) %>%
    mutate(date = ymd(as.character(date))) %>%
    filter(date >= ymd("2022-02-26")) %>%             # get exactly 180 days of data
    # mutate(price = as.double(price)) %>%
    drop_na()

COHORT ANALYSIS

Get Range of Initial Purchases 

cdnow_first_purchase_tbl <- cdnow_tbl %>%
    group_by(customer_id) %>%
    slice_min(date) %>%
    ungroup()

cdnow_first_purchase_tbl %>%
    pull(date) %>%
    range()

## [1] "2022-02-26" "2022-08-25"

Set Cohort Span

Set initial purchase: 1/26/2022 - 5/27/2022

ids_in_cohort <- cdnow_first_purchase_tbl %>%
    filter_by_time(
        .start_date = "2022-02-26",
        .end_date   = "2022-05-27"
    ) %>%
    distinct(customer_id) %>%
    pull(customer_id)

cdnow_cohort_tbl <- cdnow_tbl %>%
    filter(customer_id %in% ids_in_cohort)

Visualize: Spend Distribution 

tidymodels_prefer()

cdnow_cohort_tbl %>%
    select(price) %>%
    filter(price > 1000) %>%
    ggplot(aes(x = price)) +
    geom_histogram(binwidth = 250, col = "white")

cdnow_cohort_tbl %>%
    select(price) %>%
    filter(price > 0) %>%
    ggplot(aes(x = price)) +
    geom_histogram(bins = 50, col = "white") +
    scale_x_log10()

ymin <- min(cdnow_cohort_tbl$price)

y25 <- quantile(cdnow_cohort_tbl$price, 0.25)

y50 <- median(cdnow_cohort_tbl$price)

y75 <- quantile(cdnow_cohort_tbl$price, 0.75)

ymax <- max(cdnow_cohort_tbl$price)

iqr <- y75 - y25

upper_fence <- y75 + 8 * iqr

cdnow_cohort_tbl <- cdnow_cohort_tbl %>%
    mutate(price = ifelse(price > upper_fence, upper_fence, price))

cdnow_cohort_tbl %>% skimr::skim()
Name Piped data
Number of rows 39503
Number of columns 3
_______________________
Column type frequency:
character 1
Date 1
numeric 1
________________________
Group variables None

Table 1: Data summary

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
customer_id 0 1 4 8 0 22397 0

Variable type: Date

skim_variable n_missing complete_rate min max median n_unique
date 0 1 2022-02-26 2022-08-25 2022-04-25 181

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
price 0 1 150.26 236.42 0 0 50 180 1620 ▇▁▁▁▁

Visualize: Total Cohort Purchases 

cdnow_cohort_tbl %>%
    summarize_by_time(
        total_price = sum(price, na.rm = TRUE),
        .by   = "month"
    ) %>%
    plot_time_series(date, total_price, .y_intercept = 0)

Visualize: Individual Customer Purchases 

n    <- 1:10
ids  <- unique(cdnow_cohort_tbl$customer_id)[n]

cdnow_cohort_tbl %>%
    filter(customer_id %in% ids) %>%
    group_by(customer_id) %>%
    plot_time_series(
        date, price,
        .y_intercept = 0,
        .smooth      = FALSE,
        .facet_ncol  = 2,
        .interactive = FALSE,
        .title = "Customer Purchase Behavior"
    ) +
    geom_point(color = "#2c3e50")

MACHINE LEARNING

Questions:

  • What will the customers spend in the next 90-Days?
  • What is the probability of a customer to make a purchase in next 90-days?

Splitting into Groups (2-Stages)

  • 1: Random Splitting by Customer ID
set.seed(123)
ids_train <- cdnow_cohort_tbl %>%
    pull(customer_id) %>%
    unique() %>%
    sample(size = round(0.8*length(.))) %>%
    sort()

split_1_train_tbl <- cdnow_cohort_tbl %>%
    filter(customer_id %in% ids_train)

split_1_test_tbl  <- cdnow_cohort_tbl %>%
    filter(!customer_id %in% ids_train)
  • 2: Time Splitting
splits_2_train <- time_series_split(
    split_1_train_tbl,
    assess     = "90 days",
    cumulative = TRUE
)

splits_2_train %>%
    tk_time_series_cv_plan() %>%
    plot_time_series_cv_plan(date, price)

splits_2_test <- time_series_split(
    split_1_test_tbl,
    assess     = "90 days",
    cumulative = TRUE
)

splits_2_test %>%
    tk_time_series_cv_plan() %>%
    plot_time_series_cv_plan(date, price)

FEATURE ENGINEERING (RFM)

Make in-sample targets from training data

targets_train_tbl <- testing(splits_2_train) %>%
    group_by(customer_id) %>%
    summarise(
        spend_90_total = sum(price)
        # ,
        # spend_90_flag    = 1
    ) %>%
    mutate(spend_90_flag = ifelse(spend_90_total > 0, 1, 0))

Make out-sample targets from testing (splits_2)

targets_test_tbl <- testing(splits_2_test) %>%
    group_by(customer_id) %>%
    summarise(
        spend_90_total = sum(price)
        # ,
        # spend_90_flag    = 1
    ) %>%
    mutate(spend_90_flag = ifelse(spend_90_total > 0, 1, 0))

Make Training Data

  • RFM: Recency, Frequency, Monetary
max_date_train <- training(splits_2_train) %>%
    pull(date) %>%
    max()

train_tbl <- training(splits_2_train) %>%
    group_by(customer_id) %>%
    summarise(
        recency   = (max(date) - max_date_train) / ddays(1),
        frequency = n(),
        price_sum   = sum(price, na.rm = TRUE),
        price_mean  = mean(price, na.rm = TRUE)
    ) %>%
    left_join(
        targets_train_tbl
    ) %>%
    replace_na(replace = list(
        spend_90_total = 0,
        spend_90_flag  = 0
    )
    ) %>%
    mutate(spend_90_flag = as.factor(spend_90_flag))

Make Testing Data

  • Repeat for testing data
  • Need full customer history: training splits 1 and 2
test_tbl <- training(splits_2_test) %>%
    group_by(customer_id) %>%
    summarise(
        recency     = (max(date) - max_date_train) / ddays(1),
        frequency   = n(),
        price_sum   = sum(price, na.rm = TRUE),
        price_mean  = mean(price, na.rm = TRUE)
    ) %>%
    left_join(
        targets_test_tbl
    ) %>%
    replace_na(replace = list(
        spend_90_total = 0,
        spend_90_flag  = 0
    )
    ) %>%
    mutate(spend_90_flag = as.factor(spend_90_flag))

RECIPES

Model 1: 90-Day Spend Prediction

recipe_spend_total <- recipe(spend_90_total ~ ., data = train_tbl) %>%
    step_center() %>%
    step_rm(spend_90_flag, customer_id)

Model 2: 90-Day Spend Probability

recipe_spend_prob <- recipe(spend_90_flag ~ ., data = train_tbl) %>%
    step_center() %>%
    step_rm(spend_90_total, customer_id)

recipe_spend_prob %>% prep() %>% juice() %>% glimpse()

## Rows: 17,918
## Columns: 5
## $ recency       <dbl> -21, -1, -11, -34, -75, -37, -9, -42, -22, -42, -23, -3,…
## $ frequency     <int> 1, 2, 4, 6, 2, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1,…
## $ price_sum     <dbl> 129.00, 178.00, 366.40, 417.66, 187.95, 129.00, 129.00, …
## $ price_mean    <dbl> 129.0000, 89.0000, 91.6000, 69.6100, 93.9750, 129.0000, …
## $ spend_90_flag <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,…

summary(recipe_spend_prob)

## # A tibble: 7 × 4
##   variable       type    role      source  
##   <chr>          <chr>   <chr>     <chr>   
## 1 customer_id    nominal predictor original
## 2 recency        numeric predictor original
## 3 frequency      numeric predictor original
## 4 price_sum      numeric predictor original
## 5 price_mean     numeric predictor original
## 6 spend_90_total numeric predictor original
## 7 spend_90_flag  nominal outcome   original

MODELS

Model 1: 90-Day Spend Prediction

wflw_spend_total_xgb <- workflow() %>%
    add_model(
        boost_tree(
            mode = "regression"
        ) %>%
            set_engine("xgboost")
    ) %>%
    add_recipe(recipe_spend_total) %>%
    fit(train_tbl)

Model 2: 90-Day Spend Probability

wflw_spend_prob_xgb <- workflow() %>%
    add_model(
        boost_tree(
            mode = "classification"
        ) %>%
            set_engine("xgboost")
    ) %>%
    add_recipe(recipe_spend_prob) %>%
    fit(train_tbl)

TEST SET EVALUATION

Make Test Predictions

predictions_test_tbl <-  bind_cols(
  predict(wflw_spend_total_xgb, test_tbl) %>%
    rename(.pred_total = .pred),
  
  predict(wflw_spend_prob_xgb, test_tbl, type = "prob") %>%
    select(.pred_1) %>%
    rename(.pred_prob = .pred_1)
) %>%
  bind_cols(test_tbl) %>%
  select(starts_with(".pred"), starts_with("spend_"), everything())

Model Test Accuracy 

predictions_test_tbl %>%
    yardstick::mae(spend_90_total, .pred_total)

## # A tibble: 1 × 3
##   .metric .estimator .estimate
##   <chr>   <chr>          <dbl>
## 1 mae     standard        54.2

predictions_test_tbl %>%
    yardstick::roc_auc(spend_90_flag, .pred_prob, event_level = "second")

## # A tibble: 1 × 3
##   .metric .estimator .estimate
##   <chr>   <chr>          <dbl>
## 1 roc_auc binary         0.694

predictions_test_tbl %>%
    yardstick::roc_curve(spend_90_flag, .pred_prob, event_level = "second")%>%
    autoplot()

FEATURE IMPORTANCE

Probability Model 

vip(wflw_spend_prob_xgb$fit$fit,
    aesthetics = list(color = "grey50", fill = "grey50"))

Spend Model 

vip(wflw_spend_total_xgb$fit$fit,
    aesthetics = list(color = "grey50", fill = "grey50"))

SAVE WORK

fs::dir_create("cust/artifacts")

wflw_spend_prob_xgb %>% write_rds("cust/artifacts/bus_model_prob.rds")
wflw_spend_total_xgb %>% write_rds("cust/artifacts/bus_model_spend.rds")

vi_model(wflw_spend_prob_xgb$fit$fit) %>% write_rds("cust/artifacts/bus_vi_prob.rds")
vi_model(wflw_spend_total_xgb$fit$fit) %>% write_rds("cust/artifacts/bus_vi_spend.rds")

all_tbl <- bind_rows(train_tbl, test_tbl)
predictions_all_tbl <- bind_cols(
  predict(wflw_spend_total_xgb, all_tbl) %>%
    rename(.pred_total = .pred),
  predict(wflw_spend_prob_xgb, all_tbl, type = "prob") %>%
    select(.pred_1) %>%
    rename(.pred_prob = .pred_1)
) %>%
  bind_cols(all_tbl) %>%
  select(starts_with(".pred"), starts_with("spend_"), everything())

predictions_all_tbl %>% write_rds("cust/artifacts/bus_predictions_all_tbl.rds")

PUTTING THE ANALYSIS TO WORK

Which customers have the highest spend probability in next 90-days?

  • Target for new products similar to what they have purchased in the past
predictions_test_tbl %>%
    arrange(desc(.pred_prob))

## # A tibble: 4,435 × 9
##    .pred_total .pred_p…¹ spend…² spend…³ custo…⁴ recency frequ…⁵ price…⁶ price…⁷
##          <dbl>     <dbl>   <dbl> <fct>   <chr>     <dbl>   <int>   <dbl>   <dbl>
##  1     20570.      0.902    5638 1       A413626     -14      18 12062.   670.  
##  2      2422.      0.890    6420 1       A400706      -2      10  6026.   603.  
##  3     11042.      0.858    4133 1       A405766     -11      12  7145    595.  
##  4       138.      0.681       0 0       C136131      -3       4    69     17.2 
##  5       139.      0.681       0 0       N10028…      -3       8    61.9    7.74
##  6      4387.      0.672    6075 1       A412193     -23       9  2539    282.  
##  7       101.      0.615    7260 1       A413713     -21       7  2400    343.  
##  8        37.7     0.574       0 0       583305      -31       2    60     30   
##  9        52.2     0.565       0 0       N11489…      -1       4   124.    31.0 
## 10        24.4     0.538       0 0       112925       -3       1   120    120   
## # … with 4,425 more rows, and abbreviated variable names ¹​.pred_prob,
## #   ²​spend_90_total, ³​spend_90_flag, ⁴​customer_id, ⁵​frequency, ⁶​price_sum,
## #   ⁷​price_mean

Which customers have recently purchased but are unlikely to buy?

  • Incentivize actions to increase probability
  • Provide discounts, encourage referring a friend, nurture by letting them know what’s coming
predictions_test_tbl %>%
  filter(recency    > -50,
         .pred_prob < 0.2) %>%
  arrange(.pred_prob)

## # A tibble: 1,950 × 9
##    .pred_total .pred_p…¹ spend…² spend…³ custo…⁴ recency frequ…⁵ price…⁶ price…⁷
##          <dbl>     <dbl>   <dbl> <fct>   <chr>     <dbl>   <int>   <dbl>   <dbl>
##  1       10.9     0.0267       0 0       106169      -46       1     129     129
##  2       10.9     0.0267       0 0       127142      -45       1     129     129
##  3       10.9     0.0267       0 0       323222      -45       1     129     129
##  4       10.9     0.0267       0 0       749954      -46       1     129     129
##  5       10.9     0.0267       0 0       N314572     -45       1     129     129
##  6       10.9     0.0267       0 0       N684914     -46       1     129     129
##  7       10.9     0.0267       0 0       N693650     -45       1     129     129
##  8       10.9     0.0267       0 0       N890694     -45       1     129     129
##  9       11.6     0.0270       0 0       100062      -28       1     129     129
## 10        8.94    0.0270       0 0       100301      -36       1     129     129
## # … with 1,940 more rows, and abbreviated variable names ¹​.pred_prob,
## #   ²​spend_90_total, ³​spend_90_flag, ⁴​customer_id, ⁵​frequency, ⁶​price_sum,
## #   ⁷​price_mean

Missed opportunities: Big spenders that could be targeted

predictions_test_tbl %>%
    arrange(desc(.pred_total)) %>%
    filter(
        spend_90_total == 0
    )

## # A tibble: 3,891 × 9
##    .pred_total .pred_p…¹ spend…² spend…³ custo…⁴ recency frequ…⁵ price…⁶ price…⁷
##          <dbl>     <dbl>   <dbl> <fct>   <chr>     <dbl>   <int>   <dbl>   <dbl>
##  1       8309.    0.367        0 0       N13077…     -16       4   2318     580.
##  2       5745.    0.0485       0 0       N12976…     -26       3   2337     779 
##  3       1016.    0.285        0 0       N845735     -50       5   1406.    281.
##  4        592.    0.141        0 0       A414303     -71       1   1620    1620 
##  5        293.    0.169        0 0       N13085…     -11       4   2756     689 
##  6        231.    0.126        0 0       N255594     -11       3   1520.    507.
##  7        223.    0.269        0 0       N12648…      -8       6   1245     208.
##  8        203.    0.399        0 0       N525750     -19       3   1296.    432.
##  9        203.    0.390        0 0       N647911      -7       3   1337.    446.
## 10        181.    0.0755       0 0       N700036      -7       1   1620    1620 
## # … with 3,881 more rows, and abbreviated variable names ¹​.pred_prob,
## #   ²​spend_90_total, ³​spend_90_flag, ⁴​customer_id, ⁵​frequency, ⁶​price_sum,
## #   ⁷​price_mean

prediction_tbl_1 <- readr::read_rds("cust/artifacts/bus_predictions_all_tbl.rds")

prediction <-prediction_tbl_1 %>%
    arrange(desc(.pred_total)) %>%
    filter(spend_90_total < 0.6 * .pred_total) %>%
    filter(.pred_total > 45) %>%
    select(spend_90_total,  .pred_total, customer_id, recency, frequency, price_sum, price_mean) %>%

    rename(
        "90-Day Spend (Predict)"      = .pred_total,
        "90-Day Spend (Actual)"       = spend_90_total,
        # "Predicted Spend Probability" = .pred_prob,
        "Cust ID"                     = customer_id,
        "Monetary (Total)"            = price_sum,
        "Monetary (Avg)"              = price_mean
    ) %>%
    rename_all(
        .funs = ~ str_replace_all(., "_", " ") %>%
            str_to_title()

    )

big_spenders <- prediction %>%
    # filter("90-Day Spend (Predict)" >= 150.00) %>%
    gt() %>%
    tab_header(
        title = md("**Business A -** Customer Analytics"),
        subtitle = md("**Predicted Big Spenders**")
    ) %>%
    fmt_number(
        columns = c(Recency, Frequency)
    ) %>%
    fmt_currency(
        columns = c("90-Day Spend (Actual)", "90-Day Spend (Predict)",
                    "Monetary (Total)", "Monetary (Avg)")
    ) %>%
    fmt_passthrough(
        columns = c("Cust Id")
    ) %>%
    tab_source_note(
        source_note = md("Source: Tealium EventDB")
    )

big_spenders

Business A - Customer Analytics
Predicted Big Spenders
90-Day Spend (Actual) 90-Day Spend (Predict) Cust Id Recency Frequency Monetary (Total) Monetary (Avg)
$5,638.00 $20,569.82 A413626 −14.00 18.00 $12,061.65 $670.09
$4,133.00 $11,041.65 A405766 −11.00 12.00 $7,145.00 $595.42
$0.00 $8,309.12 N1307794 −16.00 4.00 $2,318.00 $579.50
$0.00 $5,744.53 N1297639 −26.00 3.00 $2,337.00 $779.00
$0.00 $1,016.45 N845735 −50.00 5.00 $1,405.50 $281.10
$0.00 $592.05 A414303 −71.00 1.00 $1,620.00 $1,620.00
$0.00 $544.94 A414239 −15.00 3.00 $4,018.72 $1,339.57
$0.00 $544.94 A418833 −14.00 3.00 $3,649.39 $1,216.46
$0.00 $536.99 A416472 −44.00 5.00 $6,057.00 $1,211.40
$0.00 $488.12 N1302902 −49.00 7.00 $4,193.00 $599.00
$0.00 $451.70 592784 −35.00 2.00 $3,240.00 $1,620.00
$0.00 $451.70 A415096 −51.00 2.00 $3,240.00 $1,620.00
$0.00 $451.70 A415574 −45.00 2.00 $3,240.00 $1,620.00
$0.00 $388.61 A414095 −17.00 4.00 $6,355.00 $1,588.75
$0.00 $366.98 N1256879 −35.00 4.00 $2,952.00 $738.00
$0.00 $301.98 550441 −64.00 2.00 $3,240.00 $1,620.00
$0.00 $301.98 A406823 −60.00 2.00 $3,240.00 $1,620.00
$0.00 $292.81 N1308533 −11.00 4.00 $2,756.00 $689.00
$0.00 $263.10 921479 −86.00 1.00 $1,620.00 $1,620.00
$0.00 $263.10 N1298770 −77.00 1.00 $1,620.00 $1,620.00
$0.00 $263.10 NA400407 −77.00 1.00 $1,620.00 $1,620.00
$0.00 $240.20 A418839 −45.00 1.00 $1,620.00 $1,620.00
$0.00 $240.20 N1281289 −56.00 1.00 $1,620.00 $1,620.00
$0.00 $238.22 N1309866 −1.00 4.00 $2,492.00 $623.00
$0.00 $237.61 N1306239 −14.00 3.00 $2,303.73 $767.91
$129.00 $232.09 A416356 −2.00 3.00 $1,239.50 $413.17
$0.00 $230.98 N1307003 −4.00 5.00 $1,577.28 $315.46
$0.00 $230.98 N255594 −11.00 3.00 $1,520.26 $506.75
$0.00 $223.03 N1264896 −8.00 6.00 $1,245.00 $207.50
$0.00 $203.19 N525750 −19.00 3.00 $1,295.95 $431.98
$0.00 $203.19 N647911 −7.00 3.00 $1,337.20 $445.73
$0.00 $197.22 N1142504 −2.00 10.00 $1,393.48 $139.35
$0.00 $184.45 N1119903 −12.00 9.00 $1,746.05 $194.01
$0.00 $182.25 A415592 −30.00 4.00 $6,480.00 $1,620.00
$0.00 $180.87 A418878 −9.00 1.00 $1,620.00 $1,620.00
$0.00 $180.87 N700036 −7.00 1.00 $1,620.00 $1,620.00
$0.00 $176.56 N1194007 −20.00 4.00 $1,596.00 $399.00
$0.00 $176.56 N1297310 −17.00 3.00 $1,620.00 $540.00
$0.00 $176.56 N644234 −23.00 4.00 $1,518.40 $379.60
$0.00 $157.30 753629 −27.00 4.00 $1,227.72 $306.93
$0.00 $157.30 N1306236 −24.00 3.00 $1,223.00 $407.67
$0.00 $157.30 N1303156 −30.00 3.00 $1,259.00 $419.67
$0.00 $157.30 N1305353 −33.00 3.00 $1,223.00 $407.67
$0.00 $154.72 A409962 −85.00 4.00 $1,308.90 $327.23
$0.00 $154.72 N1116008 −61.00 3.00 $1,227.95 $409.32
$0.00 $148.17 95611 −36.00 2.00 $2,384.30 $1,192.15
$0.00 $147.22 A415825 −18.00 5.00 $2,300.00 $460.00
$0.00 $141.01 96469 −25.00 2.00 $3,240.00 $1,620.00
$0.00 $141.01 A406484 −15.00 2.00 $3,240.00 $1,620.00
$0.00 $141.01 A407334 −1.00 2.00 $3,240.00 $1,620.00
$0.00 $141.01 252123 −30.00 2.00 $3,240.00 $1,620.00
$0.00 $140.09 N1304340 −32.00 3.00 $1,591.00 $530.33
$0.00 $138.91 568399 −3.00 1.00 $0.00 $0.00
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$0.00 $50.60 N580406 −1.00 2.00 $31.96 $15.98
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$0.00 $50.60 N644626 −1.00 1.00 $0.00 $0.00
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$0.00 $50.60 N997371 −2.00 1.00 $0.00 $0.00
$0.00 $47.80 252131 −16.00 3.00 $1,720.00 $573.33
$0.00 $47.80 N1112390 −17.00 3.00 $1,689.00 $563.00
$0.00 $46.46 N990511 −27.00 3.00 $1,727.00 $575.67
Source: Tealium EventDB
Posted on:
November 27, 2022
Length:
29 minute read, 6085 words
Tags:
machine learning
See Also:
Bootstrapped Resampling Regression & Revenue Forecasting
Predicting chocolate bar ratings