[R] Using spline parameters to generate data

[Spencer Graves]

1.  Did you plot the data within subsets to evaluate the appropriateness 
of any particular model?

2.  Did you previously use "nls" to estimate parameters in the 
exponential model to appropriate subsets of the data?  If yes, did you 
make various plots of residuals, e.g., vs. predicted to evaluate lack of 
fit, normal probability plots (qqnorm) to evaluate the distribution of 
residuals, and absolute values of residuals vs. predicted to evaluate 
homogeniety of variance.

3.  Only if residual plots suggest lack of fit would I abandon the 
exponential model.  Even then, I would be loath to embrace splines just 
because they are too unconstrained and not tied to any theoretical model 
of the phenomena of interest.  What does available theory tell you about 
possible functional forms for the model?  If an exponential does not 
hold in part of the regions of interest, what alternative functional 
forms might be suggested by the available theory?

4.  Have you also made qqplots, e.g., qqnorm, of parameters estimated 
from model fits?  My preference is to look for normality everywhere it 
make physical sense in the application, to transform, e.g., with 
logarithms or logits or probits or log(-log(yield)), where the transform 
would more likely be normal [possibly adding a small constant or 
multiplying by a number close to 1 to avoid taking logarithm of 0]. 
Then I use rnorm rather than runif.

hope this helps.
spencer graves

chumpmonkey3 at hushmail.com wrote:
> # Sorry for the confussion.
> # The way I had originally generated the data was
> # sort of like this (cut and paste the code below a few times):
> 
> foo.curve <- runif(1,0.8,1.2) * exp(runif(1,-0.015,-0.005) * 1:500) +
> runif(1,0.25,0.75) 
> ts.plot(foo.curve, lwd = 2)
> 
> # where the min and max values in runif() were mined from the data using
> nls.
> # Are there similar ways to manipulate the smooth spline parameters to
> give that kind of data?
> # I still need a smooth line but would like the nugget, sill and range
> to change 
> # (to borrow terms from semivariance)
> 
> On Thu, 14 Aug 2003 17:46:28 -0700 Spencer Graves <spencer.graves at PDF.COM>
> wrote:
> 
>>Have you considered adding noise to "predict(spline.model)$y"?  If
>>this 
>>won't solve your problem, then I think I don't understand what you
>>want 
>>to do.
>>
>>spencer graves
>>
>>chumpmonkey3 at hushmail.com wrote:
>>
>>># I need to generate some data. I'm modeling some time series
>>
>>that follow
>>
>>>a
>>># negative exponential decay (mostly). I have 20 samples that
>>
>>can easily
>>
>>>be fit with cubic splines.
>>># What I want to do is generate many thousands of similar samples
>>
>>using
>>
>>>the parameters from the splines
>>>
>>># For instance one data sample looks not unlike this:
>>>foo.curve <- 1 * exp(-0.01 * 1:500) + 0.5 
>>>ts.plot(foo.curve, lwd = 2)
>>>
>>># Another sample looks not unlike this:
>>>foo.curve2 <- 0.9 * exp(-0.02 * 1:500) + 0.5 
>>>ts.plot(foo.curve2, lwd = 2)
>>>
>>>
>>>
>>># They can be fit with splines easily like so:
>>>
>>>ts.plot(foo.curve, lwd = 2)
>>>spline.model <- smooth.spline(foo.curve)
>>>
>>>fits4foo <- predict(spline.model)$y
>>>spline4foo <- spline(1:500, fits4foo)
>>>lines(spline4foo$x, spline4foo$y, col = "red", lwd = 2, lty =
>>
>>"dashed")
>>
>>># I originally generated the data I needed by using a nls model
>>
>>and 
>>
>>># adding some noise to the mean of the coefficents from those
>>
>>fits.
>>
>>># However, I've been told to try and do this using splines for
>>
>>arcane
>>
>>>reasons.
>>>
>>># So, if you had 20 splines like spline.model above and wanted
>>
>>to generate
>>
>>>some similar data what would you do?
>>># Thanks in advance.
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
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>>>
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>>
>>
>>
>>
> 
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