Skip to main content

data - Fitting multiple datasets to the same nonlinear model


Perhaps a rather simple question, but the suggested questions seem to all be covering something slightly different. What I have can be described as follows.


One takes a dataset, call it Data; it has dimensions 10 by 1000 by 2 lets say, which is to say it is 10 arrays of {x,y} data of length 1000.



Now I know the following about it: it behaves according to a model Model[x,a,b,c]. Moreover, all 10 arrays have the same a,bbut not the same cparameter. What I am interested in is how one does a NonLinearModelFit over such a dataset, fitting a,b,c1...c10 in a single go. I should note that I have an initial value array cinit of dimensions 10 as well.


One way I thought of that should in principle work is with KroneckerDelta; I could prepend each dataset with some coordinate that I could use in addition to x and then make a model with the deltafunctions, but this feels very sloppy. There should be an easy way, should there not?


I would post the full model and the data I am working with, but not only is it a big dataset, the parameters and the model are still very much undetermined. I think it would make the question rather offtopic as it is my job to figure out the parameters, not you. So I thought it would make sense to just stick to the concept.



Answer



Here is a crude way to do it. First the dataset id is appended to the 1000 x 10 x 2 data array. Then the function you have is modified to create a dummy variable vector and the dot product is used to select the parameter of interest: c1, c2, c3,...., or c10.


(* Number of different values of c *)
nc = 10;
(* Number of observations per dataset *)
n = 1000; 


(* Create some data for a 1000 x 10 x 2 array *)
xx = Table[i/n, {i, n}];
data = Table[
   Transpose[{xx, 
     5 + 2 xx + xx^2 + RandomVariate[NormalDistribution[0, 1], n]}], {i, nc}];

(* Add in dataset number: 1 through nc *)
data2 = Flatten[
   Table[{i, data[[i, j, 1]], data[[i, j, 2]]}, {i, nc}, {j, n}], 1];


model[x_, a_, b_, i_, c_] := Module[{d, j},
   (* Create dummy variables *)
   d = Table[If[j == i, 1, 0], {j, Length[c]}];
   (* Determine function value *)
   a + b x + (c.d) x^2];

nlm = NonlinearModelFit[data2, 
   model[x, a, b, z, nc, {c1, c2, c3, c4, c5, c6, c7, c8, c9, c10}],
   {a, b, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10}, {z, x}];
nlm["BestFitParameters"]

(* {a -> 4.99484, b -> 1.93603, c1 -> 1.18239, c2 -> 1.0829, 
 c3 -> 1.21282, c4 -> 1.06046, c5 -> 1.13936, c6 -> 1.07549, 
 c7 -> 1.01086, c8 -> 0.960816, c9 -> 0.979848, c10 -> 1.03909} *)

But note that I get a warning:



Experimental`NumericalFunction::dimsl: {x} given in {z,x} should be a list of dimensions for a particular argument.



Also, besides assuming common values for a and b , you are also assuming a common error variance. Residuals should be checked to see if there are any departures from that assumption or if a more complex error structure is warranted.


Comments

Post a Comment

Popular posts from this blog

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]
Post a Comment
Read more

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]
Post a Comment
Read more

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1....
Post a Comment
Read more