The very rigid constraints of a chemical model form a framework within which the fit is confined and which results in a robust analysis, in model-free analysis, this framework is dramatically wider and looser and these methods suffer gradually from a sever lack of robustness. It must be remembered, however, that the choice of the wrong model necessarily results in the rung analysis and wrong resulting parameters.
Model Based Analyses
Simple first order kinetics
d[A]dt
= -k [A]
A Bk
[A] = [A]0 exp (-kt)
[B] = [A]0 (1 - exp (-kt))
[A]0=1
k=0.2
Suppose A=1.3 & k=0.25
A=440 = A [A]0 exp (-kt) + r^
How one can determine the parameters of the model?
RSS =(ri2)
RSS =0.15
Suppose A=1.3 & k=0.25
A=440 = A [A]0 exp (-kt) + r^
How one can determine the parameters of the model?
0 2 4 6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
1
Time
Abs
orba
nce
Suppose A=1.0 & k=0.20
RSS =1.42 × 10-5
How one can determine the parameters of the model?
A=440 = A [A]0 exp (-kt) + r^
Selective multivariate dataA1 = A1 {[A]0 exp (-kt)} + r1
= +A1
A2 = A2 {[A]0 exp (-kt)} + r2
= +A2
=
A1 A2
+
400 420 440 460 480 500 520 540 560 580 6000
0.2
0.4
0.6
0.8
1
1.2
1.4
Wavelength
Abs
orba
nce
400 420 440 460 480 500 520 540 560 580 6000
0.2
0.4
0.6
0.8
1
1.2
1.4
Wavelength (nm)
Abs
orba
nce
In the absence of selectivity
A Bk
A = C ET + R
At each non-selective region
=
A A A A A A
B B B B B B
C = f(k)
R = A – C C+ A
R = f(k)