[R] Help with nonlinear regressional

Daniel Malter daniel at umd.edu
Tue Sep 2 22:51:46 CEST 2008

With that you should probably get advice from your local stats department.
Although you describe your procedure, we do not know your data. And in
particular, we do not know what you do in R. 

Just from inspecting your graph, it looks that your estimated function
undershoots/overshoots the fitted values systematically for certain
intervals of the fit. For example, over the entire last part of the fitted
curve, the actual data points lie predominantly above the fitted curve and
for a long interval before that they lie predominantly below the fitted
curve. This should not be so, which indicates that your fitted function,
despite its relative fit, may not reflect your data generating process well.

Regarding fixing the function in the first observation/data point: That's
wrong. This point would then carry an infinitely greater amount of
information than all the other points (because you assume zero error for
this point). Just imagine you would have a second point like this somewhere
else on the timeline. Then you could perfectly fit your nonlinear function
with two data points. You could only do that if your first point is
nonstochastic, i.e. if there is no error and you would get the EXACT same
value at that point in time every time you run your experiment.

Again, I think it's a question the definition of your function.


cuncta stricte discussurus

-----Ursprüngliche Nachricht-----
Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im
Auftrag von LuriFax
Gesendet: Tuesday, September 02, 2008 8:06 AM
An: r-help at r-project.org
Betreff: [R] Help with nonlinear regressional

Dear All,

I am doing experiments in live plant tissue using a laser confocal
microscope. The method is called "fluorescence recovery after
photo-bleaching"  (FRAP) and here follows a short summary:

1. Record/ measure fluorescence intensity in a defined, round region of
interest (ROI, in this case a small spot) to determine the initial intensity
value before the bleaching. This pre-bleach value is also used for
normalising the curve (pre-bleach is then set to 1).

2. Bleach this ROI (with high laser intensity).

3. Record/ measure the recovery of fluorescence over time in the ROI until
it reaches a steady state (a plateau).
n. Fit the measured intensity for each time point and mesure the half time
(the timepoint which the curve has reached half the plateau), and more...

The recovery of fluorescence in the ROI is used as a measurement of protein
diffusion in the time range of the experiment. A steep curve means that the
molecules has diffused rapidly into the observed ROI and vice versa.

When I do a regressional curve fit without any constraints I get a huge
deviation from the measured value and the fitted curve at the first data
point in the curve (se the bottom picture).

My question is simply: can I constrain the fitting so that the first point
used in fitting is equal to the measured first point? Also, is this method
of fitting statistically justified / a correct way of doing it when it comes
to statistical error? 

Since the first point in the curve is critical for the calculation of the
halftime I get a substantial deviation when I compare the halftime from a
"automatically" fitted curve (let software decide) and a fitting with a
constrained first-point (y0).

I assume that all measured values have the same amount of noise and
therefore it seems strange that the first residual deviates that strongly
(the curve fit is even not in the range of the standard deviation of the
first point). 

I will greatly appreciate some feedback. Thank you.

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