Pfthb

How do researchers include additional predictors/independent variables when estimating the bass curve? I've read that Bass diffusion does not accept additional predictors, but yet I see papers claiming that they do. With that said, is this possible with the nls() function in R? I have created some toy data and an example without the extra predictor, advert.

TIA

library(data.table)

options(scipen=999)
rm(list=ls())

df <- data.table(
 year = seq(1979, 1988, by=1), 
 T = 1:10, 
 sales = c(840, 1470, 2110, 4000, 7590, 10950, 10530, 9470, 7790, 5890),
 advert = c(100,100,100,100,100,75,75,50,50,25))
df[, sales_cumulative := cumsum(sales)]

est_bass <- nls(sales ~ M*(((P+Q)^2/P)*exp(-(P+Q)*T))/(1+(Q/P)*exp(-(P+Q)*T))^2,
 # add P and Q below
 start=c(list(M = 60630, P = 0.03, Q = 0.38)),
 data = df)
coef(est_bass)

# P, Q, M parameters
m = coef(est_bass)[1]
p = coef(est_bass)[2]
q = coef(est_bass)[3]

Tdelt <- (1:100)/10
ngete <- exp(-(p+q)*Tdelt)

# plot pdf
par(mfrow=c(1,2))

Bpdf <- m*((p+q)^2/p)*ngete/(1+(q/p)*ngete)^2
plot(Tdelt, Bpdf, xlab = "Year from 1979", ylab = "Sales per year", type = "l")
points(df$T, df$sales) # compare to original

# plot cdf
Bcdf <- m*(1-ngete)/(1+(q/p)*ngete)
plot(Tdelt, Bcdf, xlab = "Year from 1979", ylab = "Cumulative sales", type = "l")
points(df$T, df$sales_cumulative)