diffusion (version 0.2.7)

seqdiffusion: Enables fitting various sequential diffusion curves.

Description

This function fits diffusion curves of the type "bass", "gompertz" or gsgompertz across generations. Parameters are estimated for each generation individually by minimising the Mean Squared Error with the subplex algorithm from the nloptr package. Optionally p-values of the coefficients can be determined via bootstraping. Furthermore, the bootstrapping allows to remove insignificant parameters from the optimisation process.

Usage

seqdiffusion(x, 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 seqdiffusion, which contains:

• type diffusion model type used

• diffusion returns model specification for each generation (see diffusion for details)

• call calls function fitted

• w named matrix of fitted parameters for each generation

• x matrix of actuals

• mse insample Mean Squared Error for each generation

• pval all p-values for w at each generation

Arguments

x

matrix containing in each column the adoption per period for generation k

cleanlead

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

prew

the w of the previous generation. This is used for sequential fitting.

l

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

cumulative

If TRUE optimisation is done on cumulative adoption.

pvalreps

bootstrap repetitions to estimate (marginal) p-values

eliminate

if TRUE eliminates insignificant parameters from the estimation. Forces pvalreps = 1000 if left to 0.

sig

significance level used to eliminate parameters

verbose

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

type

of 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. #' @param maxiter number of iterations the optimser takes (default == 10000 for "nm" and Inf for "hj")

opttol

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

w

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

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

plot.seqdiffusion and print.seqdiffusion.

Examples

  fit <- seqdiffusion(tsIbm)
  plot(fit)