bass function

Bass Model

Fits the Bass Diffusion model. In particular, fits an observed curve of proportions of adopters to $F(t)$, the proportion of adopters at time $t$, finding the corresponding coefficients $p$, Innovation rate, and $q$, imitation rate.

fitbass(dat, ...)

## S3 method for class 'diffnet'
fitbass(dat, ...)

## Default S3 method:
fitbass(dat, ...)

## S3 method for class 'diffnet_bass'
plot(
  x,
  y = 1:length(x$m$lhs()),
  add = FALSE,
  pch = c(21, 24),
  main = "Bass Diffusion Model",
  ylab = "Proportion of adopters",
  xlab = "Time",
  type = c("b", "b"),
  lty = c(2, 1),
  col = c("black", "black"),
  bg = c("lightblue", "gray"),
  include.legend = TRUE,
  ...
)

bass_F(Time, p, q)

bass_dF(p, q, Time)

bass_f(Time, p, q)

Arguments

• dat: Either a diffnet object, or a numeric vector. Observed cumulative proportion of adopters.
• ...: Further arguments passed to the method.
• x: An object of class diffnet_bass.
• y: Integer vector. Time (label).
• add: Passed to matplot.
• pch: Passed to matplot.
• main: Passed to matplot.
• ylab: Character scalar. Label of the y axis.
• xlab: Character scalar. Label of the x axis.
• type: Passed to matplot.
• lty: Passed to matplot.
• col: Passed to matplot.
• bg: Passed to matplot.
• include.legend: Logical scalar. When TRUE, draws a legend.
• Time: Integer vector with values greater than 0. The $t$ parameter.
• p: Numeric scalar. Coefficient of innovation.
• q: Numeric scalar. Coefficient of imitation.

Returns

An object of class nls and diffnet_bass. For more details, see nls in the stats package.

Details

The function fits the bass model with parameters $[p, q]$ for values $t = 1, 2, \dots, T$, in particular, it fits the following function:

Which is implemented in the bass_F function. The proportion of adopters at time $t$, $f(t)$ is:

and it's implemented in the bass_f function.

For testing purposes only, the gradient of $F$ with respect to $p$

and $q$ is implemented in bass_dF.

The estimation is done using nls.

Examples

# Fitting the model for the Brazilian Farmers Data --------------------------
data(brfarmersDiffNet)
ans <- fitbass(brfarmersDiffNet)

# All the methods that work for the -nls- object work here
ans
summary(ans)
coef(ans)
vcov(ans)

# And the plot method returns both, fitted and observed curve
plot(ans)

References

Bass's Basement Institute Institute. The Bass Model. (2010). Available at: https://web.archive.org/web/20220331222618/http://www.bassbasement.org/BassModel/. (accessed live for the last time on March 29th, 2017.)

See Also

Other statistics: classify_adopters(), cumulative_adopt_count(), dgr(), ego_variance(), exposure(), hazard_rate(), infection(), moran(), struct_equiv(), threshold(), vertex_covariate_dist()

Author(s)

George G. Vega Yon