seqdiffusion: Enables fitting various sequential diffusion curves.

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

Description

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 p-values of the coefficients can be determined via bootstraping. Furthermore, the bootstrapping allows to remove insignificant parameters from the optimisation process.

Usage

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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", "weibull"), optim = c("nm", "hj"), maxiter = Inf,
  opttol = 1e-06)

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.

Value

Returns an object of class seqdiffusion, which contains:

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.

Weibull

The initialisation is obatained through by a linear approximation median-ranked OLS described in Sharif and Islam 1980.

Author(s)

Oliver Schaer, [email protected],

Nikoloas Kourentzes, [email protected]

References

See Also

plot.seqdiffusion and print.seqdiffusion.

Examples

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  fit <- seqdiffusion(tsIbm)
  plot(fit)

mamut86/diffusion documentation built on May 21, 2019, 11:22 a.m.