distances: Special distances for 'adoption'

In adoption: Modelling Adoption Process in Marketing

Description

Distance function given here are defined for the sole use within the model definition for adoption. These functions increase the processing speed in adoption.

THESE FUNCTIONS SHOULD NEVER BE USED OUTSIDE THE MODEL DEFINITION FOR adoption. THEY SHOULD BE USED ONLY IN THE SAME WAY AS GIVEN IN THE EXAMPLES OF adoption, WITHOUT ANY MODIFICATIONS!

Usage

  GoldenbergDistance(param, dist, W, Goldenberg_C)
  VarDistance(param, dist, W)

Arguments

param	the weight parameter. For the Goldenberg distance it has (at least) two parameters; for the VAR distance it has one parameter.
dist	the matrix for Euclidean distances between the coordinates that are given by the function coord in the model definition.
W	A square matrix of size m, where m is the market size. Because of this argument, (nearly) any arbitrary use of the distance function will crash the whole system! Within adoption the correct size of the matrix will be passed.
Goldenberg_C	Some large constant, e.g. 1e6

Details

DO NOT USE THESE FUNCTIONS OUTSIDE THE MODEL DEFINITIONS FOR adoption.

Value

NULL

Note

Since these distance function modify the values of the argument W by reference, the use of these distance functions will nearly always lead to a system crash if these functions are used wrongly. However, it is save to use them in the model definition for defining the weight function, e.g.,

weight = function(param, dist, W)
GoldenbergDistance(param, dist, W, Goldenberg_C)

which equivalent to (but much faster than)

weight = function(param, dist) {
neighbour <- dist <= param[1]
diag(neighbour) <- 0
neighbour / Goldenberg_C
}

Note that the weight is, in the first piece of code, defined with an additional argument W more, which refers to a matrix of correct size in adoption.

Examples

Goldenberg <- list( ## model by Goldenberg, Libai, Muller (2010)
    m = 1000L,
    repetitions=10L,
    dt = 1,
    relative.instance = 0.2,
    SOCIAL = c(1, 5, 5),
    PRIVATE = c(5, 1, 5),
    Ic.start = function(param, m, rep, ...) {
      m * rnorm(m * rep, param[1], prod(param[1:2]))
    },
    Ic = function(param, Nt, m, start) {
      Inf * (2 * (Nt > start) - 1) ## start has size m * rep, i.e. Nt is
      ##                                   recycled
    },
    Ic.param = c("mean h" = 0.02,
		 "sigma" = 0.4),
    Ic.param.min = c(0.005, 0.08),
    Ic.param.max = c(0.1, 1.5),
    
    coord = function(param, m) {
      if (param[1] == 1) as.matrix(1:m)
      else {
	m2 <- ceiling(sqrt(m))
	m3 <- ceiling(m / m2)
	as.matrix(expand.grid(1:m2, 1:m3))[1:m, ]
      }},
    coord.param = c(dim = 2),
    weight =  function(param, dist, W) {
      GoldenbergDistance(param, dist, W, 1e6)
    },
 
    weight.param.min = 1.5,
    weight.param.max = 1.5,
    weight.param = c("max distance d"=1.5),
 
    Utrafo = function(U, threshold, ...) 1e6 * as.double(U>=threshold),
    
    Uthreshold = 0, ## here: constant for any people; we might
    Uthreshold.min = 0,
    Uthreshold.max = 0,
    Up.start = function(param, m, rep) rep(-1, m * rep),
    Up = function(param, m, nT, rep, ...) {
      pmax(-1e6 + 1,
	   -log(runif(nT * rep * m)/(1-param[1])) / log(1-param[2]))
      },
    Up.param = c(prob_a=0.1, prob_b=0.1),
    Up.param.min = c(0.005, 0.05),
    Up.param.max = c(0.99, 0.99),
    
    "MAX/PLUS OPERATORS" = rep(5, 3),
    alpha = c("alpha_1"=0, "alpha_2"=1),
    alpha.min = c(0, 1),
    alpha.max = c(0, 1),
    beta = c("beta_1"=1, "beta_2"=1),
    beta.min = c(1, 1),
    beta.max = c(1, 1),
    gamma = c("gamma_1"=0.5, "gamma_2"=0.5),
    gamma.min = c(0.5, 0.5),
    gamma.max = c(0.5, 0.5)
 )

RFoptions(cores=2)  ## see package RandomFieldsUtils
print(adoption(Goldenberg, join_models=FALSE, buttons2right=TRUE,
               gui=interactive()))

adoption documentation built on Sept. 23, 2021, 5:11 p.m.