netdiffuseR (version 1.22.6)

bass: 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 diffnet
fitbass(dat, ...)
# S3 method for default
fitbass(dat, ...)
# S3 method for 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)

Value

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

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.

Author

George G. Vega Yon

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.

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)