[R] confidence intervals for nls or nls2 model

[Gabor Grothendieck]

On Tue, May 15, 2012 at 8:08 PM, Francisco Mora Ardila
<fmora at oikos.unam.mx> wrote:
> Hi all
>
> I have fitted a model usinf nls function to these data:
>
>> x
>  [1]   1   0   0   4   3   5  12  10  12 100 100 100
>
>> y
>  [1]  1.281055090  1.563609934  0.001570796  2.291579783  0.841891853
>  [6]  6.553951324 14.243274230 14.519899320 15.066473610 21.728809880
> [11] 18.553054450 23.722637370
>
> The model fitted is:
>
> modellogis<-nls(y~SSlogis(x,a,b,c))
>
> It runs OK. Then I calculate confidence intervals for the actual data using:
>
> dataci<-predict(as.lm(modellogis), interval = "confidence")
>
> BUt I don´t get smooth curves when plotting it, so I want to get other "confidence
> vectors" based on a new x vector by defining a new data to do predictions:
>
> x0 <-  seq(0,15,1)
> dataci<-predict(as.lm(modellogis), newdata=data.frame(x=x0), interval = "confidence")
>
> BUt it does not work: I get the same initial confidence interval
>
> Any ideas on how to get tconfidence and prediction intervals using new X data on a
> previous model?
>

as.lm is a linear model between the response variable and the gradient
of the nonlinear model and as we see below x is not part of that
linear model so x can't be in newdata when predicting from the tangent
model.  We can only make predictions at the original x points.   For
other x's we could use Interpolation. See ?approx  (?spline can also
work in smooth cases but in the example provided the function has a
kink and that won't work well with splines.)

> as.lm(modellogis)$model
              y          a             b             c  (offset)
1   1.281055090 0.06601796 -4.411829e-01  1.168928e+00  1.397153
2   1.563609934 0.04798815 -3.268846e-01  9.766080e-01  1.015584
3   0.001570796 0.04798815 -3.268846e-01  9.766080e-01  1.015584
4   2.291579783 0.16311227 -9.767241e-01  1.597189e+00  3.451981
5   0.841891853 0.12203013 -7.665928e-01  1.512752e+00  2.582551
6   6.553951324 0.21464369 -1.206154e+00  1.564573e+00  4.542552
7  14.243274230 0.74450055 -1.361047e+00 -1.455630e+00 15.756031
8  14.519899320 0.59707858 -1.721353e+00 -6.770205e-01 12.636107
9  15.066473610 0.74450055 -1.361047e+00 -1.455630e+00 15.756031
10 21.728809880 1.00000000 -2.943955e-13 -9.073765e-12 21.163223
11 18.553054450 1.00000000 -2.943955e-13 -9.073765e-12 21.163223
12 23.722637370 1.00000000 -2.943955e-13 -9.073765e-12 21.163223

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