Description Usage Arguments Value Bass curve Gompertz curve Gamma/Shifted Gompertz Weibull Author(s) References See Also Examples
This function fits diffusion curves of the type "bass"
,
"gompertz"
, gsgompertz
or weibull
across generations.
Parameters are estimated for each generation individually by minimising the
Mean Squared Error with the subplex algorithm from the nloptr package.
Optionally pvalues of the coefficients can be determined via bootstraping.
Furthermore, the bootstrapping allows to remove insignificant parameters from
the optimisation process.
1 2 3 4 5 
x 
matrix containing in each column the adoption per period for generation k 
cleanlead 
removes leading zeros for fitting purposes (default == T) 
prew 
the 
l 
the lnorm (1 is absolute errors, 2 is squared errors) 
cumulative 
If TRUE optimisation is done on cumulative adoption. 
pvalreps 
bootstrap repetitions to estimate (marginal) pvalues 
eliminate 
if TRUE eliminates insignificant parameters from the
estimation. Forces 
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 NelderMeade or
"hj" for HookeJeeves. #' @param maxiter number of iterations the optimser
takes (default == 
opttol 
Tolerance for convergence (default == 1.e06) 
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 pvalues 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 nonexponential 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.
The initialisation is obatained through by a linear approximation medianranked OLS described in Sharif and Islam 1980.
Oliver Schaer, [email protected],
Nikoloas 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), 215227.
Bemmaor, A. 1994. Modeling the Diffusion of New Durable Goods: WordofMouth Effect versus Consumer Heterogeneity. In G. Laurent, G.L. Lilien and B. Pras (Eds.). Research Traditions in Marketing. Boston: Kluwer, pp. 201223.
Jukic, D., Kralik, G. and Scitovski, R., 2004. Leastsquares fitting Gompertz curve. Journal of Computational and Applied Mathematics, 169, 359375.
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, 247256.
plot.seqdiffusion
and print.seqdiffusion
.
1 2  fit < seqdiffusion(tsIbm)
plot(fit)

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