data/model quantities |
Ra(t), Rt(t) |
fraction of all users that adopt/terminate the service in a time window |
Rn(t) = Ra(t) − Rt(t) |
net rate of adoption |
empirical quantities |
ta, tt
|
time of adoption/termination of service for a user |
|
lifetime of a user account in the service |
Δt
|
time window used to define rates |
I |
number of Internet users in a country at the end of observation period |
Na(t) |
number of service users at time t
|
pa(t), pp(t) |
rate of spontaneous/peer-pressure adoption at time t
|
,
|
rate of spontaneous/peer-pressure termination at time t
|
|
rate of termination at time t
|
p(n) |
probability that a user adopts, if a fraction n of its neighbours are adopters |
prand(n) |
value of p(n) after shuffling adoption times |
Δp(n) = p(n) − prand(n) |
unbiased measure of social influence in adoption |
τ |
inverse speed of innovation diffusion |
model parameters |
pa, pp
|
constant probability of spontaneous/peer-pressure adoption |
ps, pr
|
constant probability of temporary/permanent termination |
〈k〉 |
average degree of network |
|
peer-pressure adoption probability, weighted by degree |
estimated parameters |
|
estimates of average degree and asymptotic rate of termination |
|
estimate of temporary termination probability |