[R] Problems with nls

[Daniel Malter]

Those are in fact the coefficients for p and q they are estimating, though
their M is different. Who knows what they did with that. 

The data source was:

Title:	Diffusion models of mobile telephony in Greece
Source: Telecommunications policy [0308-5961] Michalakelis yr:2008 vol:32
iss:3-4 pg:234



Gabor Grothendieck wrote:
> 
> On Wed, Jun 15, 2011 at 6:05 PM, Daniel Malter <daniel at umd.edu>
> wrote:
>> There may be two issues here. The first might be that, if I understand
>> the
>> Bass model correctly, the formula you are trying to estimate is the
>> adoption
>> in a given time period. What you supply as data, however, is the
>> cumulative
>> adoption by that time period.
>>
>> The second issue might be that the linear algorithm may fail and that it
>> may
>> be preferable to use Newton-Raphson (the standard) as this may provide
>> better values in the iterations.
>>
>> If you do both, i.e., you do NLS on period adoption and use
>> Newton-Raphson,
>> you get an estimate. Though, I am of course not sure whether that is
>> "correct" in the sense that it is what you would expect to find.
>>
>>
>> adoption <-
>> c(167000,273000,531000,938000,2056452,3894103,5932090,7963742,9314687,10469060,11393302,11976340)
>> time <- seq(from = 1,to = 12, by = 1)
>>
>> adoption2<-c(0,adoption[1:(length(adoption)-1)])
>> S<-(adoption-adoption2)/max(adoption)
>>
>> ## Models
>> Bass.Model <- S ~ M*((p + q)^2/p) * (exp(-(p + q) * time)/((q / p) *
>> exp(-(p + q) * time) + 1)^2)
>> ## Starting Parameters
>> Bass.Params <- list(p = 0.1, q = 0.1, M=1)
>> ## Model fitting
>> Bass.Fit <- nls(formula = Bass.Model, start = Bass.Params)
>> summary(Bass.Fit)
>>
> 
> If your hypothesis regarding the cumulative vs. adoptions is correct
> then it may be that poster wants this:
> 
>> S <- diff(adoption)
>> time <- seq_along(S)
>> Bass2 <- S ~ m * ((p + q)^2/p) * (exp(-(p + q) * time)/((q / p) *
> + exp(-(p + q) * time) + 1)^2)
>> nls(formula = Bass2, start = c(p = 0.03, q = 0.4, m = max(S)))
> Nonlinear regression model
>   model:  S ~ m * ((p + q)^2/p) * (exp(-(p + q) * time)/((q/p) *
> exp(-(p +      q) * time) + 1)^2)
>    data:  parent.frame()
>                 p                 q                 m
> 8.65635536465e-03 6.52817192695e-01 1.23485254536e+07
>  residual sum-of-squares: 321990186229
> 
> Number of iterations to convergence: 16
> Achieved convergence tolerance: 8.10600476229e-06
> 
>> # or equivalently in terms of "plinear" where S, time and Bass2 are
>> # as written just above
>> m <- 1 # set m to 1 since we are using .lin instead
>> nls(formula = Bass2, start = c(p = 0.03, q = 0.4), alg = "plinear")
> Nonlinear regression model
>   model:  S ~ m * ((p + q)^2/p) * (exp(-(p + q) * time)/((q/p) *
> exp(-(p +      q) * time) + 1)^2)
>    data:  parent.frame()
>                 p                 q              .lin
> 8.65637919209e-03 6.52816636341e-01 1.23485299874e+07
>  residual sum-of-squares: 321990186247
> 
> Number of iterations to convergence: 9
> Achieved convergence tolerance: 5.6090474901e-06
> 
> 
> 
> 
> -- 
> Statistics & Software Consulting
> GKX Group, GKX Associates Inc.
> tel: 1-877-GKX-GROUP
> email: ggrothendieck at gmail.com
> 
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