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Re: I: NONLINEARMODELFIT
*To*: mathgroup at smc.vnet.net
*Subject*: [mg120314] Re: I: NONLINEARMODELFIT
*From*: Ray Koopman <koopman at sfu.ca>
*Date*: Mon, 18 Jul 2011 06:15:00 -0400 (EDT)
*References*: <ivuc83$gta$1@smc.vnet.net>
On Jul 17, 3:06 am, maria giovanna dainotti
<mariagiovannadaino... at yahoo.it> wrote:
> Dear Mathematica Group,
>
> I am fitting a function of 3 parameters with the NonlinearModelFit
> and with the Marquardt Levemberg algorithm. Since this method gives
> the interval of the Parameters of the best fit considering the parameters
> not correlated, I was looking for a tool that takes into account the
> fact that the parameters are correlated and the parameters interval
> should respect the following rule:
>
> The confidence interval for a given parameter should be computed by
> varying the parameter value until the chi^2 increases by a particular
> amount above the minimum, or best-fit value. The amount that the chi
> square is allowed to increase (also referred to as the critical
> delta_chi^2) depends on the confidence level one requires, and on
> the number of parameters whose confidence space is being calculated.
> The critical delta_chi^2 for common cases are given in Avni, 1976:
> For example in the case I am using for 3 parameters delta_chi^2=3.50.
>
> I would be very grateful if someone of you is acquainted with a such
> a tool in Mathematica or some of you has done a code to sort this
> problem out. Thanks a lot in advance for your help.
>
> Best regards,
>
> Maria
https://groups.google.com/group/sci.stat.edu/browse_frm/thread/5eef0a33244e080f?hl=en#
discusses a similar problem. Here is the code I used.
In[1]:=
color = {"Blue","Brown","Green","Orange","Red","Yellow"};
{k,n} = {Length@#,Tr@#}&[f = {127, 63, 122, 147, 93, 76}];
e = Array[x,k];
init = Transpose@{e,f-1,f+1};
b[\[Alpha]_] = Tr[f^2/e] == n + 2 InverseGammaRegularized[(k-1)/2,
\[Alpha]] && And@@Thread[e > 0] && Tr@e == n;
In[6]:=
" 95% Limits\nColor Lower Upper\n" <>
ToString@PaddedForm[TableForm[Table[{color[[j]],
First@NMinimize[{x[j],b[.05]},init]/n,
First@NMaximize[{x[j],b[.05]},init]/n},{j,k}],
TableSpacing->{0,1}],{4,3}]
Out[6]=
95% Limits
Color Lower Upper
Blue 0.154 0.261
Brown 0.067 0.147
Green 0.147 0.252
Orange 0.183 0.295
Red 0.107 0.201
Yellow 0.084 0.171
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