diffusion (version 0.2.7)

diffusion: Fit various diffusion curves.

Description

This function fits diffusion curves that can be of "bass", "gompertz" or "gsgompertz" type.

Usage

diffusion(x, w = NULL, cleanlead = c(TRUE, FALSE), prew = NULL, l = 2,
  cumulative = c(TRUE, FALSE), pvalreps = 0, eliminate = c(FALSE, TRUE),
  sig = 0.05, verbose = c(FALSE, TRUE), type = c("bass", "gompertz",
  "gsgompertz"), optim = c("nm", "hj"), maxiter = Inf, opttol = 1e-06)

Value

Returns an object of class diffusion, which contains:

• type diffusion curve type used

• call calls function fitted

• w named vector of fitted parameters

• x 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

Arguments

x

vector with adoption per period

w

vector of curve parameters (see note). If provided no estimation is done.

cleanlead

removes leading zeros for fitting purposes (default == TRUE)

prew

Experimental. Ignore!

l

the l-norm (1 is absolute errors, 2 is squared errors).

cumulative

If TRUE optimisation is done on cumulative adoption.

pvalreps

Experimental. Ignore!

eliminate

Experimental. Ignore!

sig

Experimental. Ignore!

verbose

if TRUE console output is provided during estimation (default == FALSE)

type

diffusion curve to use. This can be "bass", "gompertz" and "gsgompertz"

optim

optimization method to use. This can be "nm" for Nelder-Meade or "hj" for Hooke-Jeeves.

maxiter

number of iterations the optimser takes (default == 10000 for "nm" and Inf for "hj")

opttol

Tolerance for convergence (default == 1.e-06)

Bass curve

The optimisation of the Bass curve is initialisated by the linear aproximation suggested in Bass (1969).

Gompertz curve

The initialisation of the Gompertz curve uses the approach suggested by Jukic et al. (2004), but is adapted to allow for the non-exponential version of Gompertz curve. This makes the market potential parameter equivalent to the Bass curves's and the market potential from Bass curve is used for initialisation.

Gamma/Shifted Gompertz

The curve is initialised 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.

Author

Oliver Schaer, ,

Nikoloas Kourentzes,

References

• 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.

See Also

predict.diffusion, plot.diffusion and print.diffusion.

Examples

 fitbass <- diffusion(tsChicken[, 2], type = "bass")
 fitgomp <- diffusion(tsChicken[, 2], type = "gompertz")
 fitgsg <- diffusion(tsChicken[, 2], type = "gsgompertz")
 
 # Produce some plots
 plot(fitbass)
 plot(fitgomp)
 plot(fitgsg)