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. ----------------------- http://www.nabble.com/file/p19268931/CurveFit_SigmaPlot.png -- View this message in context: http://www.nabble.com/Help-with-nonlinear-regressional-tp19268931p19268931.html Sent from the R help mailing list archive at Nabble.com.
LuriFax wrote:> > > 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). >Note that this is a text-only list; most people cannot see your figure, I read it on Nabble where it is possible to view the data LuriFax wrote:> > My question is simply: can I constrain the fitting so that the first point > used in fitting is equal to the measured first point? >Yes, you can. Normalize all points by dividing through the first data point, and fit the model with a fixed initial value set to 1. LuriFax wrote:> > Also, is this method of fitting statistically justified / a correct way of > doing it when it comes to statistical error? >No, no, no, don't do it. We have similar curves from gastric emptying (http://www.menne-biomed.de/gastempt/index.html), and 20 years ago some authority recommended that method of clamping to the first data point. With the effect that American medical journals, who usually do not have statistical referees (British do), simply refuse to publish anything that does not follow that advice. If you look carefully, it is not the first point that is wrong, but there is to much tension in the fit so that the first part as a whole is off. So you have two choices: Either accept the slight deviation of the fit; or add another parameter. If you have many sets of data, and can use nlme to give "borrowing strength", the latter approach could work. If you have only one curve, be careful when adding another parameter. With nls, it is not that dangerous because this brutal function simply refuses to converge when there is too much correlation between coefficients. With SigmaPlot, you can end up with seeminglingly good fits; only when you look at the coefficient StdDevs, you may note that these are 3.0 plus/minus 4000 or so! Dieter -- View this message in context: http://www.nabble.com/Help-with-nonlinear-regressional-tp19268931p19270899.html Sent from the R help mailing list archive at Nabble.com.
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. Best, Daniel ------------------------- cuncta stricte discussurus ------------------------- -----Urspr?ngliche 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. ----------------------- http://www.nabble.com/file/p19268931/CurveFit_SigmaPlot.png -- View this message in context: http://www.nabble.com/Help-with-nonlinear-regressional-tp19268931p19268931.h tml Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.