statistical comparison of exponential association fits
- From: "us " <us@xxxxxxxxxxxxxxx>
- Date: Wed, 10 Sep 2008 16:43:03 +0000 (UTC)
dear CSSM members
INTRO
i realize that this is not simply about ML syntax...
however, i was hoping that one of this NG's visitors might have an enlightening insight on how to solve the problem, which stems from the realm of eye movement biology, using entirely ML tools...
TASK
the snippet below simulates 4 different two-parameter exponential association curves
y = a * (1 - exp(-x/b));
and fits them (using the curve fitting tbx)...
the simulations and (first order) results are displayed; all other resulting statistical data are saved...
% exponential association model
m=fittype('a*(1-exp(-x/b))');
% simulation parameters
av=[100,101,100,110]; % <- sim: a values
bv=[5,5,2,5]; % <- sim: b values
rs=2; % <- sim: uniform noise width
sp=[100,5]; % <- fit: common start point
ns=numel(av); % <- #simulations
x=(.1:.1:20).';
y=nan(size(x,1),ns);
% simulation
clear b c;
a=cell(ns,1);
res=nan(ns,6);
leg=cell(1,ns);
% - create data sets
% - fit each set
for i=1:ns
y(:,i)=av(i).*(1-exp(-x/bv(i)))+rs*(rand(size(x))-.5);
[a{i,1},b(i),c(i)]=fit(x,y(:,i),m,'startpoint',sp);
% - save coefficients
res(i,1:2)=coeffvalues(a{i,1});
% - and 95% confidence bounds
tmp=confint(a{i});
res(i,3:end)=tmp(:).';
% - save legend entries
leg(1,i)={sprintf('a:%3d b:%1d',av(i),bv(i))};
end
% - show curves
line(x,y);
legend(leg,'location','best');
shg;
% - show results (CI-|+: low|high confidence bounds)
hdr={'a','b','aCI-','aCI+','bCI-','bCI+'};
r=[hdr;num2cell(res)];
disp(r);
%{
results of one run
'a' 'b' 'aCI-' 'aCI+' 'bCI-' 'bCI+'
[ 100] [5.0106] [99.817] [100.19] [4.9805] [5.0407]
[100.98] [4.9925] [100.79] [101.17] [4.9625] [5.0226]
[100.03] [1.9999] [ 99.93] [100.14] [1.9879] [ 2.012]
[109.99] [4.9939] [109.82] [110.17] [4.9679] [5.0199]
%}
QUESTION
which statistical procedure could one use to determine
whether two curves differ using the outputs of FIT
(-or- NLINFIT) without(!) data transformation?
dear reader please note, this is NOT a homework problem...
many a thanks to everybody who takes the time to read through this lengthy post...
urs
.
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