diffusion (version 0.4.0)

Nortonbass: Norton-Bass model

Description

Nortonbass fits a generational Bass model proposed by Norton and Bass (1987). Each subsequent generation influences the sales of the previous generation. The set of equation is estimated simulataneously.

Usage

Nortonbass(
  x,
  startval.met = c("2ST", "BB", "iBM"),
  estim.met = c("BOBYQA", "OLS", "SUR", "2SLS", "3SLS"),
  gstart = NULL,
  startval = NULL,
  flexpq = F
)

Value

coef: coefficients for p, q and m

Arguments

x

matrix or dataframe containing demand for each generation in non-cumulative form.

startval.met

Different methods of obtaining starting values.

"2ST"

Two stage approach taking "BB" method first and then re-estimate if flexpq == T (default)

"BB"

Bass and Bass (2004) method which sets \(p_{1,\dots,j} = 0.003, q_{1,\dots,j} = 0.05\) and \(m_j\) is the maximum observed value for generation \(j\)

"iBM"

Fits individual Bass models and uses this as estimators. In case flexpq == F the median of p and q is used

estim.met

Estimation method, "BOBYQA" see nlsystemfit (BOBYQA default)

gstart

optional vector with starting points of generations#'

startval

an optional Vector with starting for manual estimation

flexpq

If TRUE, generations will have independent p and q values as suggested by Islam and Maed (1997). Note that model might not converge.

Author

Oliver Schaer,

Details

For starting values the Vector values need to be named in the case flexpq == T \(p_1,\dots,p_j,q_1,\dots,q_j,m_1,\dots,m_j\). In the case of flexpq == F \(p_1, q_1, m_1,\dots, m_j\).

If gstart is not provided, the generation starting points will be detected automatically selecting the first value that is non-zero.

References

Norton, J.A. and Bass, F.M., 1987. A Diffusion Theory Model of Adoption and Substitution for Successive Generations of High-Technology Products.

Islam, T. and Meade, N., 1997. The Diffusion of Successive Generations of a Technology: A More General Model. Technological Forecasting and Social Change, 56, 49-60.

Examples

 if (FALSE) {
   fitNB1 <- Nortonbass(tsIbm, startval.met = "2ST", estim.met = "OLS",
                        startval = NULL, flexpq = F, gstart = NULL)
   fitNB2 <- Nortonbass(tsIbm, startval.met = "2ST", estim.met = "SUR",
                        startval = NULL, flexpq = F, gstart = NULL)
   # using BOBYQA algorithm
   fitNB3 <- Nortonbass(tsIbm, startval.met = "2ST", estim.met = "BOBYQA",
                        startval = NULL, flexpq = F, gstart = NULL)
   # Create some plots
   plot(tsibm[, 1],type = "l", ylim=c(0,35000))
   lines(tsibm[, 2],col ="blue")
   lines(tsibm[, 3],col ="green")
   lines(tsibm[, 4],col ="pink")
   lines(fitNB1$fit$fitted[[1]], col = "black", lty = 2)
   lines(fitNB1$fit$fitted[[2]], col = "blue", lty = 2)
   lines(fitNB1$fit$fitted[[3]], col = "green", lty = 2)
   lines(fitNB1$fit$fitted[[4]], col = "pink", lty = 2)
   lines(fitNB2$fit$fitted[[1]], col = "black", lty = 3)
   lines(fitNB2$fit$fitted[[2]], col = "blue", lty = 3)
   lines(fitNB2$fit$fitted[[3]], col = "green", lty = 3)
   lines(fitNB2$fit$fitted[[4]], col = "pink", lty = 3)
   lines(fitNB3$fit$fitted[[1]], col = "black", lty = 4)
   lines(fitNB3$fit$fitted[[2]], col = "blue", lty = 4)
   lines(fitNB3$fit$fitted[[3]], col = "green", lty = 4)
   lines(fitNB3$fit$fitted[[4]], col = "pink", lty = 4)
   # read out RMSE
   fitNB1$fit$RMSE[[1]]
   fitNB1$fit$RMSE[[2]]
   fitNB1$fit$RMSE[[3]]
   fitNB1$fit$RMSE[[4]]
   fitNB2$fit$RMSE[[1]]
   fitNB2$fit$RMSE[[2]]
   fitNB2$fit$RMSE[[3]]
   fitNB2$fit$RMSE[[4]]
   fitNB3$fit$RMSE[[1]]
   fitNB3$fit$RMSE[[2]]
   fitNB3$fit$RMSE[[3]]
   fitNB3$fit$RMSE[[4]]
 }
 # \dontshow{
   Nortonbass(tsIbm, startval.met = "2ST", estim.met = "OLS", startval = NULL, flexpq = FALSE, gstart = NULL)
 # }