seqdiffusion: Enables fitting various sequential diffusion curves.
In diffusion: Forecast the Diffusion of New Products

Description Usage Arguments Value Bass curve Gompertz curve Gamma/Shifted Gompertz Note Author(s) References See Also Examples

View source: R/seqdiffusion.R

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.

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)

`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.

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

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

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.

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.

vector w needs to be provided for the Bass curve in the order of "p", "q", "m", where "p" is the coefficient of innovation, "q" is the coeficient of imitation and "m" is the market size coefficient.

For the Gompertz curve vector w needs to be in the form of ("a", "b", "m"). 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 ("a", "b", "c", "m"). 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).

Oliver Schaer, info@oliverschaer.ch,

Nikoloas Kourentzes, nikoloas@kourentzes.com

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.

plot.seqdiffusion and print.seqdiffusion.