Package 'foretell' reference manual

Title:	Projecting Customer Retention Based on Fader and Hardie Probability Models
Description:	Project Customer Retention based on Beta Geometric, Beta Discrete Weibull and Latent Class Discrete Weibull Models.This package is based on Fader and Hardie (2007) <doi:10.1002/dir.20074> and Fader and Hardie et al. (2018) <doi:10.1016/j.intmar.2018.01.002>.
Authors:	Srihari Jaganathan
Maintainer:	Srihari Jaganathan <[email protected]>
License:	GPL-3
Version:	0.2.1
Built:	2025-01-29 19:16:15 UTC
Source:	https://github.com/sriharitn/foretell

Beta discrete Weibull (BdW) Model for Projecting Customer Retention.

Description

BdW is a beta discrete weibull model implemented based on Fader and Hardie probability based projection methedology. The survivor function for BdW is

$Beta(a,b+t^c)/Beta(a,b)$

Usage

BdW(
  surv_value,
  h,
  lower = c(0.001, 0.001, 0.001),
  upper = c(10000, 10000, 10000),
  subjects = 1000
)
BdW(
  surv_value,
  h,
  lower = c(0.001, 0.001, 0.001),
  upper = c(10000, 10000, 10000),
  subjects = 1000
)

Arguments

`surv_value`	a numeric vector of historical customer retention percentage should start at 100 and non-starting values should be between 0 and less than 100
`h`	forecasting horizon
`lower`	lower limit used in `R` `optim` rotuine. Default is `c(1e-3,1e-3)`.
`upper`	upper limit used in `R` `optim` rotuine. Default is `c(10000,10000,10000)`.
`subjects`	Total number of customers or subject default 1000

Value

`fitted:`	Fitted values based on historical data
`projected:`	Projected `h` values based on historical data
`max.likelihood:`	Maximum Likelihood of Beta discrete Weibull
`params - a`, `b and c:`	Returns a and b paramters from maximum likelihood estimation for beta distribution and c

References

Fader P, Hardie B. How to project customer retention. Journal of Interactive Marketing. 2007;21(1):76-90.

Fader P, Hardie B, Liu Y, Davin J, Steenburgh T. "How to Project Customer Retention" Revisited: The Role of Duration Dependence. Journal of Interactive Marketing. 2018;43:1-16.

Examples

surv_value <- c(100,86.9,74.3,65.3,59.3)
h <- 6
BdW(surv_value,h)

surv_value <- c(100,86.9,74.3,65.3,59.3)
h <- 6
BdW(surv_value,h)

Beta discrete Weibull (bdw) Distribution Family Function

Description

Provides functions for the probability mass function (PMF), cumulative distribution function (CDF), quantile function, and random variate generation for the BdW distribution.

Usage

dbdw(x, shape1, shape2, shape3, log = FALSE)
pbdw(x, shape1, shape2, shape3, lower.tail = TRUE, log.p = FALSE)
qbdw(p, shape1, shape2, shape3, lower.tail = TRUE, log.p = FALSE)
rbdw(n, shape1, shape2, shape3)
dbdw(x, shape1, shape2, shape3, log = FALSE)
pbdw(x, shape1, shape2, shape3, lower.tail = TRUE, log.p = FALSE)
qbdw(p, shape1, shape2, shape3, lower.tail = TRUE, log.p = FALSE)
rbdw(n, shape1, shape2, shape3)

Arguments

`x`	Vector of non-negative integers for `dbdw` and `pbdw`.
`p`	Vector of probabilities (0 <= p <= 1) for `qbdw`.
`n`	Number of random variates to generate for `rbdw`.
`shape1`	First shape parameter "a" (must be > 0).
`shape2`	Second shape parameter "b" (must be > 0).
`shape3`	Second shape parameter "c" (must be > 0).
`log`	Logical; if TRUE, probabilities are returned on the log scale (for `dsbg` and `psbg`).
`lower.tail`	Logical; if TRUE (default), probabilities are P(X <= x), otherwise P(X > x) (for `psbg`).
`log.p`	Logical; if TRUE, probabilities are returned on the log scale (for `psbg` and `qsbg`).

Value

dbdw: A numeric vector of PMF values.
pbdw: A numeric vector of CDF values.
qbdw: A numeric vector of quantile values.
rbdw: A numeric vector of random variates.

References

Fader P, Hardie B. How to project customer retention. Journal of Interactive Marketing. 2007;21(1):76-90.

Fader P, Hardie B, Liu Y, Davin J, Steenburgh T. "How to Project Customer Retention" Revisited: The Role of Duration Dependence. Journal of Interactive Marketing. 2018;43:1-16.

Examples

# PMF example
dbdw(1:5, shape1 = 2, shape2 = 3,shape3 = 0.5)

# CDF example
pbdw(1:5, shape1 = 2, shape2 = 3, shape3 = 0.5)

# Quantile example
qbdw(c(0.1, 0.5, 0.9), shape1 = 2, shape2 = 3 , shape3 = 0.5)

# Random variates
rbdw(10, shape1 = 2, shape2 = 3,  shape3 = 0.5)

# PMF example
dbdw(1:5, shape1 = 2, shape2 = 3,shape3 = 0.5)

# CDF example
pbdw(1:5, shape1 = 2, shape2 = 3, shape3 = 0.5)

# Quantile example
qbdw(c(0.1, 0.5, 0.9), shape1 = 2, shape2 = 3 , shape3 = 0.5)

# Random variates
rbdw(10, shape1 = 2, shape2 = 3,  shape3 = 0.5)

Beta Geometric (BG) Model for Projecting Customer Retention.

Description

BG is a beta geometric model implemented based on Fader and Hardie probability based projection methedology. The survivor function for BG is

$Beta(a,b+t)/Beta(a,b)$

Usage

BG(surv_value, h, lower = c(0.001, 0.001), subjects = 1000)
BG(surv_value, h, lower = c(0.001, 0.001), subjects = 1000)

Arguments

`surv_value`	a numeric vector of historical customer retention percentage should start at 100 and non-starting values should be between 0 and less than 100
`h`	forecasting horizon
`lower`	lower limit used in `R` `optim` rotuine. Default is `c(1e-3,1e-3)`.
`subjects`	Total number of customers or subject default 1000

Value

`fitted:`	Fitted values based on historical data
`projected:`	Projected `h` values based on historical data
`max.likelihood:`	Maximum Likelihood of Beta Geometric
`params - a`, `b:`	Returns a and b paramters from maximum likelihood estimation for beta distribution

References

Fader P, Hardie B. How to project customer retention. Journal of Interactive Marketing. 2007;21(1):76-90.

Examples

surv_value <- c(100,86.9,74.3,65.3,59.3)
h <- 6
BG(surv_value,h)

surv_value <- c(100,86.9,74.3,65.3,59.3)
h <- 6
BG(surv_value,h)

Observed % Customers Surviving at Least 0-12 Years

Description

A dataset containing customer retention.

Usage

data(customer_retention)
data(customer_retention)

Format

A data frame 13 observations and 3 variables.

Details

year: Time in years
regular: % of regular customers surviving
high_end: % of high_end customers surviving

References

Fader P, Hardie B. How to project customer retention. Journal of Interactive Marketing. 2007;21(1):76-90.

Excel based trendlines for projecting customer retention.

Description

exltrend generates Microsoft(r) Excel(r) based linear, logarthmic, exponential, polynomial of order 2, power trends.

Usage

exltrend(surv_value, h)
exltrend(surv_value, h)

Arguments

`surv_value`	a numeric vector of historical customer retention percentage should start at 100 and non-starting values should be between 0 and less than 100
`h`	forecasting horizon

Value

`fitted:`	A data frame of fitted Values based on historical data for linear (lin.p), exponential (exp.p), logarthmic (log.p), polynomial (poly.p) of order 2 and power (pow.p) trends.
`projected:`	A data frame of projected `h` values based on historical data for linear (lin.p), exponential (exp.p), logarthmic (log.p), polynomial (poly.p) of order 2 and power (pow.p) trends.

Examples

surv_value <- c(100,86.9,74.3,65.3,59.3)
h <- 6
exltrend(surv_value,h)

surv_value <- c(100,86.9,74.3,65.3,59.3)
h <- 6
exltrend(surv_value,h)

Latent Class Weibull (LCW) Model for Projecting Customer Retention

Description

LCW is a latent class weibull model implementation based on Fader and Hardie probability based projection methedology. The survivor function for LCW is

$wS(t|t1,c1)+(1-w)S(t|t2,c2), 0<w<1$

Usage

LCW(
  surv_value,
  h,
  lower = c(0.001, 0.001, 0.001, 0.001, 0.001),
  upper = c(0.99999, 10000, 0.999999, 10000, 0.99999),
  subjects = 1000
)
LCW(
  surv_value,
  h,
  lower = c(0.001, 0.001, 0.001, 0.001, 0.001),
  upper = c(0.99999, 10000, 0.999999, 10000, 0.99999),
  subjects = 1000
)

Arguments

`surv_value`	a numeric vector of historical customer retention percentage should start at 100 and non-starting values should be between 0 and less than 100
`h`	forecasting horizon
`lower`	lower limit used in `R` `optim` rotuine. Default is `c(0.001,0.001,0.001,0.001,0.001)`.
`upper`	upper limit used in `R` `optim` rotuine. Default is `c(0.99999,10000,0.999999,10000,0.99999)`.
`subjects`	Total number of customers or subject default 1000

Value

`fitted:`	Fitted Values based on historical data
`projected:`	Projected `h` values based on historical data
`max.likelihood:`	Maximum Likelihood of LCW
`params - t1`, `t2`, `c1`, `c2`, `w:`	Returns t1,c1,t2,c2,w paramters from maximum likelihood estimation

References

Fader P, Hardie B. How to project customer retention. Journal of Interactive Marketing. 2007;21(1):76-90.

Fader P, Hardie B, Liu Y, Davin J, Steenburgh T. "How to Project Customer Retention" Revisited: The Role of Duration Dependence. Journal of Interactive Marketing. 2018;43:1-16.

Examples

surv_value <- c(100,86.9,74.3,65.3,59.3,55.1,51.7,49.1,46.8,44.5,42.7,40.9,39.4)
h <- 6
LCW(surv_value,h)

surv_value <- c(100,86.9,74.3,65.3,59.3,55.1,51.7,49.1,46.8,44.5,42.7,40.9,39.4)
h <- 6
LCW(surv_value,h)

Drug persistency (retention) rates by different therapeutic class.

Description

A dataset containing drug persistency of patients in different therapeutic classes.

Usage

data(persistency_data)
data(persistency_data)

Format

A data frame 334 observatios and 3 variables:

therapy: Type of therapy. Unique values include: "Hypertension" "Occular Hypertension" "Statin" "Insulin" "Epilepsy" "RA" "Osteoporosis" "Alzheimer""ADHD" "Atrial Fibrillation". See references below. Data was extracted using https://automeris.io/WebPlotDigitizer/ and discretized using akima package.
time_period: Time Period
value: % Patients retained

A data frame with 334 rows and 3 variables

References

Hypertension: Solomon M, Goldman D, Joyce G, Escarce J. Cost Sharing and the Initiation of Drug Therapy for the Chronically Ill.Archives of Internal Medicine. 2009;169(8):740-748.

Occular Hypertension: Campbell J, Schwartz G, LaBounty B, Kowalski J, Patel. Patient adherence and persistence with topical ocular hypotensive therapy in real-world practice: a comparison of bimatoprost 0.01% and travoprost Z 0.004% ophthalmic solutions. Clinical Ophthalmology. 2014;8:927-935.

Statin: Kiss Z, Nagy L, Reiber I, Paragh G, Molnar M, Rokszin G et al. Persistence with statin therapy in Hungary. Archives of Medical Science. 2013;9(3):409-417.

Insulin: Roussel R, Charbonnel B, Behar M, Gourmelen J, Emery C, Detournay B. Persistence with Insulin Therapy in Patients with Type 2 Diabetes in France: An Insurance Claims Study. Diabetes Therapy. 2016;7(3):537-549.

Epilepsy: Lai E, Hsieh C, Su C, Yang Y, Huang C, Lin S et al. Comparative persistence of antiepileptic drugs in patients with epilepsy: A STROBE-compliant retrospective cohort study. Medicine. 2016;95(35):e4481.

RA: Neovius M, Arkema E, Olsson H, Eriksson J, Kristensen L, Simard J et al. Drug survival on TNF inhibitors in patients with rheumatoid arthritis comparison of adalimumab, etanercept and infliximab. Annals of the Rheumatic Diseases. 2013;74(2):354-360.

Osteoporosis: Kishimoto H, Maehara M. Compliance and persistence with daily, weekly, and monthly bisphosphonates for osteoporosis in Japan: analysis of data from the CISA. Archives of Osteoporosis. 2015;10(27):1-6.

Alzheimer: Suh D, Thomas S, Valiyeva E, Arcona S, Vo L. Drug persistency of two cholinesterase inhibitors: rivastigmine versus donepezil in elderly patients with Alzheimer's disease. Drugs & Aging. 2005;22(8):695-707.

ADHD: Beau-Lejdstrom R, Douglas I, Evans S, Smeeth L. Latest trends in ADHD drug prescribing patterns in children in the UK: prevalence, incidence and persistence. BMJ Open. 2016;6(6):1-8.

Atrial Fibrillation: Gomes T, Mamdani M, Holbrook A, Paterson J, Juurlink D. Persistence With Therapy Among Patients Treated With Warfarin for Atrial Fibrillation. Archives of Internal Medicine. 2012;172(21):1687-1689.

Shifted Beta-geometric (sbg) Distribution Family Function

Description

Provides functions for the probability mass function (PMF), cumulative distribution function (CDF), quantile function, and random variate generation for the SBG distribution.

Usage

dsbg(x, shape1, shape2, log = FALSE)
psbg(x, shape1, shape2, lower.tail = TRUE, log.p = FALSE)
qsbg(p, shape1, shape2, lower.tail = TRUE, log.p = FALSE)
rsbg(n, shape1, shape2)
dsbg(x, shape1, shape2, log = FALSE)
psbg(x, shape1, shape2, lower.tail = TRUE, log.p = FALSE)
qsbg(p, shape1, shape2, lower.tail = TRUE, log.p = FALSE)
rsbg(n, shape1, shape2)

Arguments

`x`	Vector of non-negative integers for `dsbg` and `psbg`.
`p`	Vector of probabilities (0 <= p <= 1) for `qsbg`.
`n`	Number of random variates to generate for `rsbg`.
`shape1`	First shape parameter "a" (must be > 0).
`shape2`	Second shape parameter "b" (must be > 0).
`log`	Logical; if TRUE, probabilities are returned on the log scale (for `dsbg` and `psbg`).
`lower.tail`	Logical; if TRUE (default), probabilities are P(X <= x), otherwise P(X > x) (for `psbg`).
`log.p`	Logical; if TRUE, probabilities are returned on the log scale (for `psbg` and `qsbg`).

Details

The Shifted Beta Geometric distribution with two shape parameters shape1 ( $a$ ) and shape2 ( $b$ ) has the following CDF:

$1- Beta(a,b+x)/Beta(a,b)$

For $x= 1,2,3,...,n$ and $a > 0$ and $b > 0$ .

The Shifted Beta Geometric (sBG) distribution, is a probability mixture model of Beta and Geometric distributions. sBG was introduced by Fader and Hardie, models customer retention by assuming that individuals have heterogeneous dropout probabilities. These probabilities are drawn from a Beta distribution, and each customer's retention follows a geometric process. This combination captures variability in churn behavior across a population, making it well-suited for analyzing survival data, customer lifetime and retention data.

Value

dsbg: A numeric vector of PMF values.
psbg: A numeric vector of CDF values.
qsbg: A numeric vector of quantile values.
rsbg: A numeric vector of random variates.

References

Fader P, Hardie B. How to project customer retention. Journal of Interactive Marketing. 2007;21(1):76-90.

Fader P, Hardie B, Liu Y, Davin J, Steenburgh T. "How to Project Customer Retention" Revisited: The Role of Duration Dependence. Journal of Interactive Marketing. 2018;43:1-16.

Examples

# PMF example
dsbg(1:5, shape1 = 2, shape2 = 3)

# CDF example
psbg(1:5, shape1 = 2, shape2 = 3)

# Quantile example
qsbg(c(0.1, 0.5, 0.9), shape1 = 2, shape2 = 3)

# Random variates
rsbg(10, shape1 = 2, shape2 = 3)

# PMF example
dsbg(1:5, shape1 = 2, shape2 = 3)

# CDF example
psbg(1:5, shape1 = 2, shape2 = 3)

# Quantile example
qsbg(c(0.1, 0.5, 0.9), shape1 = 2, shape2 = 3)

# Random variates
rsbg(10, shape1 = 2, shape2 = 3)

Package 'foretell'

Help Index

Beta discrete Weibull (BdW) Model for Projecting Customer Retention.

Description

Usage

Arguments

Value

References

Examples

Beta discrete Weibull (bdw) Distribution Family Function

Description

Usage

Arguments

Value

References

Examples

Beta Geometric (BG) Model for Projecting Customer Retention.

Description

Usage

Arguments

Value

References

Examples

Observed % Customers Surviving at Least 0-12 Years

Description

Usage

Format

Details

References

Excel based trendlines for projecting customer retention.

Description

Usage

Arguments

Value

Examples

Latent Class Weibull (LCW) Model for Projecting Customer Retention

Description

Usage

Arguments

Value

References

Examples

Drug persistency (retention) rates by different therapeutic class.

Description

Usage

Format

References

Shifted Beta-geometric (sbg) Distribution Family Function

Description

Usage

Arguments

Details

Value

References

Examples