[R] quadratic model with plateau

[Gabor Grothendieck]

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)))


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