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:

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

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)