[R] quadratic model with plateau

[Rolf Turner]

One other minor glitch I just noticed:

     x <- seq_along(x)

should read

     x <- seq_along(y)

     cheers,

         Rolf

On 08/04/12 10:08, Gabor Grothendieck wrote:
> On Sat, Apr 7, 2012 at 3:58 PM, Gabor Grothendieck
> <ggrothendieck at gmail.com>  wrote:
>> On Fri, Apr 6, 2012 at 9:42 PM, help ly<help.ly2005 at gmail.com>  wrote:
>>> Dear All,
>>>
>>> I would like to make a quadratic with a plateau model in R. Is there a
>>> package in R doing this? The bentcableAR package seems won't work.
>>>
>>> The link below describes what I am looking for in R exactly:
>>> http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_nlin_sect033.htm
>>>
>> Use nls directly:
>>
>> y<- c(0.46, 0.47, 0.57, 0.61, 0.62, 0.68, 0.69, 0.78, 0.7, 0.74,
>> 0.77, 0.78, 0.74, 0.8, 0.8, 0.78)
>> x<- seq_along(x)
>>
>> Mean<- function(x, alpha, beta, gamma) {
>>    pmin(alpha + beta*x + gamma*x*x, alpha - beta^2/(4 * gamma))
>> }
>> fm<- nls(y ~ Mean(x, alpha, beta, gamma), start = list(alpha = 0.45,
>> beta = 0.05, gamma = -0.0025))
>> fm
>> summary(fm)
>>
>> plot(y ~ x)
>> lines(fitted(fm) ~ x)
> It was pointed out to me offline that Mean as defined above is not
> identical to the definition in the poster's link.  Here is a revision:
>
> y<- c(0.46, 0.47, 0.57, 0.61, 0.62, 0.68, 0.69, 0.78, 0.7, 0.74,
> 0.77, 0.78, 0.74, 0.8, 0.8, 0.78)
> x<- seq_along(x)
>
> Mean<- function(x, alpha, beta, gamma) {
> 	ifelse(x<  -beta/(2 * gamma), alpha + beta*x + gamma*x*x,
> 		alpha - beta^2/(4 * gamma))
> }
> fm<- nls(y ~ Mean(x, alpha, beta, gamma), start = list(alpha = 0.45,
> beta = 0.05, gamma = -0.0025))
> fm
> summary(fm)
>
> plot(y ~ x)
> lines(fitted(fm) ~ x)
> with(as.list(coef(fm)), abline(v = -beta/(2 * gamma)))
>
>