| Title: | Forecast the Diffusion of New Products |
|---|---|
| Description: | Various diffusion models to forecast new product growth. Currently the package contains Bass, Gompertz, Gamma/Shifted Gompertz and Weibull curves. See Meade and Islam (2006) <doi:10.1016/j.ijforecast.2006.01.005>. |
| Authors: | Oliver Schaer [aut, cre] (Assistant Professor, LeBow College of Business, Drexel University, USA), Nikolaos Kourentzes [aut] (Professor of Predictive Analytics, School of Informatics, Skoevde University, Sweden), Ivan Svetunkov [aut] (Lecturer at Centre for Marketing Analytics and Forecasting, Lancaster University, UK) |
| Maintainer: | Oliver Schaer <[email protected]> |
| License: | LGPL-2.1 |
| Version: | 0.4.0 |
| Built: | 2025-03-23 05:24:41 UTC |
| Source: | https://github.com/mamut86/diffusion |
This function calculates the values of diffusion curves that can be of "bass",
"gompertz", "gsgompertz" or "weibull" type, given some parameters.
difcurve( n, w = c(0.01, 0.1, 10), type = c("bass", "gompertz", "gsgompertz", "weibull"), curve = NULL )difcurve( n, w = c(0.01, 0.1, 10), type = c("bass", "gompertz", "gsgompertz", "weibull"), curve = NULL )
n |
number of periods to calculate values for. |
w |
vector of curve parameters (see note). If argument curve is used, this is ignored. |
type |
diffusion curve to use. This can be "bass", "gompertz" and "gsgompertz". If argument curve is used, this is ignored. |
curve |
if provided |
Returns a matrix of values with each row being a period.
w needs to be provided for the Bass curve in the order of
("m", "p", "q"), where "p" is the coefficient of innovation, "q" is the
coefficient of imitation and "m" is the market size coefficient.
For the Gompertz curve, vector w needs to be in the form of
("m", "a", "b"). Where "a" is the x-axis displacement coefficient, "b"
determines the growth rate and "m" sets, similarly to Bass model, the
market potential (saturation point).
For the Shifted-Gompertz curve, vector w needs to be in the form of
("m", "a", "b", "c"). Where "a" is the x-axis displacement
coefficient, "b" determines the growth rate, "c" is the shifting parameter
and "m" sets, similarly to Bass model, the market potential (saturation
point).
For the Weibull curve, vector w needs to be in the form of
("m", "a", "b"). Where "a" is the scale parameter, "b" determines the
shape. Together, "a" and "b" determine the stepness of the curve. The "m"
parameter sets the market potential (saturation point).
Oliver Schaer, [email protected],
Nikolaos Kourentzes, [email protected]
diffusion for fitting a diffusion curve.
difcurve(w=c(0.01,0.1,10),20)difcurve(w=c(0.01,0.1,10),20)
This function fits diffusion curves that can be of "bass",
"gompertz", "gsgompertz" (Gamma/Shifted Gompertz curve) or "Weibull" type.
diffusion( y, w = NULL, cleanlead = c(TRUE, FALSE), loss = 2, cumulative = c(TRUE, FALSE), verbose = c(FALSE, TRUE), type = c("bass", "gompertz", "gsgompertz", "weibull"), method = c("L-BFGS-B", "Nelder-Mead", "BFGS", "hjkb", "Rcgmin", "bobyqa"), maxiter = 500, opttol = 1e-06, multisol = c(FALSE, TRUE), initpar = c("linearize", "preset"), mscal = c(TRUE, FALSE), ... )diffusion( y, w = NULL, cleanlead = c(TRUE, FALSE), loss = 2, cumulative = c(TRUE, FALSE), verbose = c(FALSE, TRUE), type = c("bass", "gompertz", "gsgompertz", "weibull"), method = c("L-BFGS-B", "Nelder-Mead", "BFGS", "hjkb", "Rcgmin", "bobyqa"), maxiter = 500, opttol = 1e-06, multisol = c(FALSE, TRUE), initpar = c("linearize", "preset"), mscal = c(TRUE, FALSE), ... )
y |
vector with adoption per period |
w |
vector of curve parameters (see note). Parameters set to NA will be
optimized. If |
cleanlead |
removes leading zeros for fitting purposes (default == TRUE) |
loss |
the l-norm (1 is absolute errors, 2 is squared errors). |
cumulative |
If TRUE optimisation is done on cumulative adoption. |
verbose |
if TRUE console output is provided during estimation (default == FALSE) |
type |
diffusion curve to use. This can be "bass", "gompertz" and "gsgompertz" |
method |
optimization method to use. These can be |
maxiter |
number of iterations the optimiser takes (default == |
opttol |
Tolerance for convergence (default == 1.e-06) |
multisol |
when |
initpar |
vector of initalisation parameters. If set to |
mscal |
scales market potential at initalisation with the maximum of the
observed market potential for better optimization results (default == |
... |
accepts |
Returns an object of class diffusion, which contains:
type diffusion curve type used
call calls function fitted
w named vector of fitted parameters
y actuals
fit fitted values of model
frc forecasts for future periods. This is NULL until predict.diffusion is called.
mse insample Mean Squared Error
prew the w of the previous generation
pval p-values for w
init the initial values that have been used for the optimizer
The optimization of the Bass curve is initialized by the linear approximation suggested in Bass (1969).
The initialization of the Gompertz curve uses the approach suggested by Jukic et al. (2004), but is adapted to allow for the non-exponential version of the Gompertz curve. This makes the market potential parameter equivalent to the Bass curves and the market potential from Bass curve is used for initialization.
The curve is initialized by assuming the shift operator to be 1 and becomes equivalent to the Bass curve, as shown in Bemmaor (1994). A Bass curve is therefore used as an estimator for the remaining initial parameters.
The initialization is obtained through by a linear approximation median-ranked OLS described in Sharif and Islam 1980.
vector w needs to be provided for the Bass curve in the order of
"m", "p", "q", where "p" is the coefficient of innovation, "q" is the
coefficient of imitation and "m" is the market size coefficient.
For the Gompertz curve, vector w needs to be in the form of
("m", "a", "b"). Where "a" is the x-axis displacement coefficient, "b"
determines the growth rate and "m" sets, similarly to the Bass curve, the
market potential (saturation point).
For the Shifted-Gompertz curve, vector w needs to be in the form of
("m", "a", "b", "c"). Where "a" is the x-axis displacement
coefficient, "b" determines the growth rate, "c" is the shifting parameter
and "m" sets, similarly to the Bass curve, the market potential (saturation
point).
For the Weibull curve, vector w needs to be in the form of
("m", "a", "b"). Where "a" is the scale parameter, "b" determines the
shape. Together, "a" and "b" determine the steepness of the curve. The "m"
parameter sets the market potential (saturation point).
Parameters are estimated by minimising the Mean Squared Error with a subplex algorithm from the optimx package. Optionally p-values of the coefficients can be determined via bootstraping. Furthermore, the bootstrapping allows removing insignificant parameters from the optimization process.
Oliver Schaer, [email protected],
Nikolaos Kourentzes, [email protected]
For an introduction to diffusion curves see Ord K., Fildes R., Kourentzes N. (2017) Principles of Business Forecasting 2e. Wessex Press Publishing Co., Chapter 12.
Bass, F.M., 1969. A new product growth for model consumer durables. Management Science 15(5), 215-227.
Bemmaor, A. 1994. Modeling the Diffusion of New Durable Goods: Word-of-Mouth Effect versus Consumer Heterogeneity. In G. Laurent, G.L. Lilien and B. Pras (Eds.). Research Traditions in Marketing. Boston: Kluwer, pp. 201-223.
Jukic, D., Kralik, G. and Scitovski, R., 2004. Least-squares fitting Gompertz curve. Journal of Computational and Applied Mathematics, 169, 359-375.
Sharif, N.M. and Islam, M.N. 1980. The Weibull Distribution as a General Model for Forecasting Technological Change. Technological Forecasting and Social Change, 18, 247-256.
predict.diffusion, plot.diffusion and print.diffusion.
seqdiffusion for sequential diffusion model fitting
across product generations.
fitbass <- diffusion(diff(tsChicken[, 2]), type = "bass") fitgomp <- diffusion(diff(tsChicken[, 2]), type = "gompertz") fitgsg <- diffusion(diff(tsChicken[, 2]), type = "gsgompertz") fitgwb <- diffusion(diff(tsChicken[, 2]), type = "weibull") # Produce some plots plot(fitbass) plot(fitgomp) plot(fitgsg) plot(fitgwb)fitbass <- diffusion(diff(tsChicken[, 2]), type = "bass") fitgomp <- diffusion(diff(tsChicken[, 2]), type = "gompertz") fitgsg <- diffusion(diff(tsChicken[, 2]), type = "gsgompertz") fitgwb <- diffusion(diff(tsChicken[, 2]), type = "weibull") # Produce some plots plot(fitbass) plot(fitgomp) plot(fitgsg) plot(fitgwb)
Functions to check if an object is of the specified class
is.diffusion(x) is.bass(x)is.diffusion(x) is.bass(x)
x |
The object to check. |
The list of functions includes:
is.diffusion() tests if the object was produced by a diffusion() function.
is.bass() checks if the forecast was produced by the bass() function.
TRUE if this is the specified class and FALSE otherwise.
Ivan Svetunkov, [email protected],
Oliver Schaer, [email protected]
Produces a plot of a fitted diffusion curve.
## S3 method for class 'diffusion' plot(x, cumulative = c(FALSE, TRUE), ...)## S3 method for class 'diffusion' plot(x, cumulative = c(FALSE, TRUE), ...)
x |
|
cumulative |
If TRUE plot cumulative adoption. |
... |
Unused argument. |
None. Function produces a plot.
Oliver Schaer, [email protected],
Nikolaos Kourentzes, [email protected]
fit <- diffusion(tsChicken[, 2]) plot(fit)fit <- diffusion(tsChicken[, 2]) plot(fit)
Calculates the values for h future periods of a fitted diffusion curve.
## S3 method for class 'diffusion' predict(object, h = 10, ...)## S3 method for class 'diffusion' predict(object, h = 10, ...)
object |
|
h |
Forecast horizon. |
... |
Unused argument. |
Returns an object of class diffusion, which contains:
type diffusion curve type used
call calls function fitted
w named vector of fitted parameters
y actuals
fit fitted values of model
frc forecasts for future periods.
mse insample Mean Squared Error
prew the w of the previous generation
pval p-values for w
This function populates the matrix frc of the diffusion object used as input.
Oliver Schaer, [email protected],
Nikoloas Kourentzes, [email protected]
fit <- diffusion(tsChicken[, 2]) fit <- predict(fit, 20) plot(fit)fit <- diffusion(tsChicken[, 2]) fit <- predict(fit, 20) plot(fit)
Outputs the result of a fitted diffusion curve.
## S3 method for class 'diffusion' print(x, ...)## S3 method for class 'diffusion' print(x, ...)
x |
|
... |
Unused argument. |
None. Console output only.
Oliver Schaer, [email protected],
Nikolaos Kourentzes, [email protected]
fit <- diffusion(tsChicken[, 2]) print(fit)fit <- diffusion(tsChicken[, 2]) print(fit)
A dataset containing the weekly sales of Assassins Creeds game.
A matrix with 380 observations and 8 variables
Assassins Creed 1
Assassins Creed 2
Assassins Creed 3
Assassins Creed 4
Assassins Creed 5
Assassins Creed 6
Assassins Creed 7
Assassins Creed 8
VGChartz
A dataset containing the yearly stock of cars in the Netherlands (1965-1989).
A data frame with 25 observations and 3 variables
Year
Raw stock numbers
Smoothed stock numbers as described by Franses (1994)
Franses, P.H. 1994. Fitting a Gompertz curve. Journal of Operational Research Society, 45, 109-113.
A dataset containing the average weekly female chicken weight.
A data frame with 13 observations and 2 variables
Weeks since birth
Weight of the female chicken in Kg
Jukic, D., Kralik, G. and Scitovski, R. 2004. Least-square fitting Gompertz curve. Journal of Computational and Applied Mathematics, 169, 359-375.
A dataset containing the number of confirmed COVID-19 cases in the US.
A ts object with 107 days of observations
Daily confirmed COVDID-19 cases
https://github.com/CSSEGISandData/COVID-19
COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University
A dataset containing the first four generations of yearly IBM general-purpose computers installations in the USA.
A data frame with 24 observations and 4 variables
1st generation
2nd generation (starts 6 years after first generation)
3rd generation (starts 11 years after first generation)
4th generation (starts 16 years after first generation)
Bass, P.I. and Bass, F.M. 2004. IT Waves: Two Completed Generational Diffusion Models. Working Paper Basseconomics, 1-33.
A dataset with conversion of U.S. Merchant Marine from wood to metal.
A data frame with 17 observations and 2 variables
Year
Conversion to metal
Martino, J.P. 1993. Technological Forecasting for Decision Making. 3rd edition. New York: McGraw-Hill.
A dataset containing the monthly market share of Safari browser generations from Safari 4.0 to Safari 10.
A data frame with 98 observations and 13 variables
Log file date
Usage of Windows 10
Market share of Safari browser v 10.0
Market share of Safari browser v 9.1
Market share of Safari browser v 9.0
Market share of Safari browser v 8.0
Market share of Safari browser v 7.1
Market share of Safari browser v 6.1
Market share of Safari browser v 6.0
Market share of Safari browser v 5.1
Market share of Safari browser v 5.0
Market share of Safari browser v 4.1
Market share of Safari browser v 4.0
https://gs.statcounter.com/browser-version-market-share
A dataset containing the 3WSchools monthly log files of Windows operating system usage from March 2003 until February 2017.
A data frame with 168 observations and 9 variables
Log file date
Usage of Windows 10
Usage of Windows 8
Usage of Windows 7
Usage of Windows Vista
Usage of Windows XP
Usage of Windows 2000
Usage of Windows 98
Usage of Windows 95
From March 2003 until January 2008 log file is only available bi-monthly. To retain monthly consistency, values have been linearly interpolated
https://www.w3schools.com/browsers/browsers_os.asp