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Weighting in simultaneous NonlinearModelFits

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128153] Weighting in simultaneous NonlinearModelFits
  • From: lukas.fricke at gmail.com
  • Date: Wed, 19 Sep 2012 04:57:58 -0400 (EDT)
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  • Delivered-to: l-mathgroup@wolfram.com
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I would like to add weights from a list to the problem of solving nonlinearmodelfits for different datasets / different models with equal parameters. I tried to add another counter for the weight-array index but somehow this did not work.

Code up to now:
gdata0sm = Table[gdata0[[y]], {y, startind, stopind}];
gdata1sm = Table[gdata1[[y]], {y, startind, stopind}];
gdata2sm = Table[gdata2[[y]], {y, startind, stopind}]; 
wdata0sm = Table[wdata0[[y]], {y, startind, stopind}];
wdata1sm = Table[wdata1[[y]], {y, startind, stopind}];
wdata2sm = Table[wdata2[[y]], {y, startind, stopind}];
gdata3sm = Table[gdata3[[y]], {y, startind, stopind}];
alldata = Join[gdata0sm, gdata1sm, gdata2sm];

gdata0sm looks like:
{{-206.5, 1, 1., 0.403875}, {-206., 2, 1., 0.385625}, {-205.5, 3, 1., 
  0.354828}, {-205., 4, 1., 0.287206}, {-204.5, 5, 1., 
  0.278158}, {-204., 6, 1., 0.218795}, {-203.5, 7, 1., 
  0.205412}, {-203., 8, 1., 0.181136}, {-202.5, 9, 1., 
  0.163026}, {-202., 10, 1., 0.141125}, {-201.5, 11, 1., 
  0.130676}, {-201., 12, 1., 0.12194}, {-200.5, 13, 1., 
  0.101519}, {-200., 14, 1., 0.0910204}, {-199.5, 15, 1., 
  0.0834921}, {-199., 16, 1., 0.075974}, {-198.5, 17, 1., 
  0.0714118}, {-198., 18, 1., 0.0564474}, {-197.5, 19, 1., 
  0.0507692}, {-197., 20, 1., 0.0459155}, {-196.5, 21, 1., 
  0.0403896}, {-196., 22, 1., 0.0396364}, {-195.5, 23, 1., 
  0.0328571}, {-195., 24, 1., 0.0237143}, {-194.5, 25, 1., 
  0.0294737}, {-194., 26, 1., 0.0225373}, {-193.5, 27, 1., 
  0.018375}, {-193., 28, 1., 0.0139773}, {-192.5, 29, 1., 
  0.00969231}, {-192., 30, 1., 0.0126563}, {-191.5, 31, 1., 
  0.01}, {-191., 32, 1., 0.0114706}, {-190.5, 33, 1., 
  0.00744186}, {-190., 34, 1., 0.0048}, {-189.5, 35, 1., 
  0.0059375}, {-189., 36, 1., 0.00575758}, {-188.5, 37, 1., 
  0.00901961}, {-188., 38, 1., 0.00403226}, {-187.5, 39, 1., 
  0.00454545}, {-187., 40, 1., 0.00307692}, {-186.5, 41, 1., 
  0.00357143}, {-186., 42, 1., 0.00223684}, {-185.5, 43, 1., 
  0.002}, {-185., 44, 1., 0.000806452}, {-184.5, 45, 1., 0.000769231}}

Then I define the different models with Kronecker-delta:
bfun0[a_, b_] := 1/(1 + Exp[-a*x - b]);
bfun1[a_, b_, c_, d_] := 
  Exp[c*x + d]/(1 + Exp[a*x + b])/(1 + Exp[c*x + d]);
bfun2[a_, b_, c_, d_] := 
  1 - 1/(1 + Exp[-a*x - b]) - 
   Exp[c*x + d]/(1 + Exp[a*x + b])/(1 + Exp[c*x + d]);
modtotal[index_, counter_, a_, b_, c_, d_] := 
  KroneckerDelta[index - 1]*bfun0[a, b] + 
   KroneckerDelta[index - 2]*bfun1[a, b, c, d] + 
   KroneckerDelta[index - 3]*bfun2[a, b, c, d];

and tried this expression:
thermresult = 
  NonlinearModelFit[alldata, 
   modtotal[index, counter, a, b, c, 
    d], {{a, -.28}, {b, -58}, {c, -.82}, {d, -150}}, {x, counter, 
    index}, Weights -> (If[#3 == 1, 1/(wdata0sm[[#2]])^2, 
       If[#3 == 2, 1/(wdata1sm[[#2]])^2, 1/(wdata2sm[[#2]])^2]] &)];

This works fine with constant weights (replace each reference to an array by a fixed number), but not in the way I tried it...

Thanks a lot for any advice!



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