bass: Bass Model

In srdyal/diffusiontest: Analysis of Diffusion and Contagion Processes on Networks

Bass Model

Description

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.

Usage

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.

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:

F(t) = \frac{1 - \exp{-(p+q)t}}{1 + \frac{q}{p}\exp{-(p+q)t}}

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

f(t) = \left\{\begin{array}{ll} F(t), & t = 1 \\ F(t) - F(t-1), & t > 1 \end{array}\right.

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.

Value

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

Author(s)

George G. Vega Yon

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()

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)

srdyal/diffusiontest documentation built on Dec. 9, 2024, 1:14 a.m.